Mechanical strength of tibial trabecular bone evaluated by X-ray computed tomography

The prospects for the use of quantitative computed tomography (QCT) for evaluation of mechanical properties of tibial trabecular bone were investigated. Computed tomography (CT) data from the proximal tibial epi- and metaphysis of six human cadaver knees were correlated with mechanical data obtained from compression tests and penetration strength measurements. In addition CT and intraoperative penetration data were compared in 20 patients. If spatial agreement between CT and mechanical measurement sites is optimized, close correlations are found between the relative linear attenuation coefficient determined by CT and the ultimate strength (r = 0.84), the yield strength (r = 0.85), the elastic modulus (r = 0.78), the ultimate energy absorption (r = 0.83), the yield energy absorption (r = 0.81), and the penetration strength (r = 0.82). It is concluded that these correlations are sufficient to make QCT a valuable tool for non-invasive evaluation of the spatial distribution of bone properties in several clinical applications.     

Assessing the accuracy of high-resolution X-ray computed tomography of primate trabecular bone by comparisons with histological sections

Different lines of evidence suggest that trabecular bone architecture contains a functional signal related to an organism's locomotor behavior. An understanding of the interspecific and intraspecific variation in extant nonhuman primate trabecular structure is needed to evaluate its usefulness as a tool to reconstruct the locomotor habits of extinct primates. High-resolution X-ray computed tomography (HRXCT) is a new imaging approach with a resolution in the tens of microns that allows nondestructive access to the internal structure of bony elements. Previous studies indicate that such resolution is necessary to accurately quantify structural parameters of trabecular bone. The primary goal of this study was to test the accuracy of HRXCT by comparing stereological measurements from HRXCT images and histological thin sections of cancellous bone taken from the proximal femur and humerus of baboons. To this end, 11 bone samples were scanned on an HRXCT scanner and then thin-sectioned to reveal the scanned plane. HRXCT images were thresholded using a modified half-maximum height protocol. The stereological measurements included bone volume fraction (BV/TV), trabecular number (Tb.N), bone surface to volume ratio (BS/BV), trabecular thickness (Tb.Th), and trabecular spacing (Tb.Sp). The measurement errors on the HRXCT images were 10.90% for BV/TV, 6.06% for Tb.N, 14.19% for BS/BV, 14.33% for Tb.Th, and 7.09% for Tb.Sp, but none of these measurements were significantly different from the histological standards (alpha = 0.05). A second goal of this study was to examine the influence of thresholding, a necessary step in any morphometric study using computed tomography, on the accuracy of the quantitative morphometry. Threshold values derived from a modified half-maximum height protocol showed that parameters derived from the region of interest (area in which stereological measurements were later taken) produced better reconstructions of the actual bone structure than threshold values derived from more inclusive areas of bone. We conclude that HRXCT can accurately reconstruct the complex architecture of trabecular bone, and that thresholding is a nontrivial step in trabecular bone studies, with even slight changes in the protocol greatly affecting the morphometric data. HRXCT represents a valuable analytical tool that should be of interest to a great many researchers in physical anthropology because it allows nondestructive access to internal morphology, thereby preserving valuable and limited skeletal collections.     

Three-axial strain controlled testing applied to bone specimens from the proximal tibial epiphysis

Reproducibility of the determination of Young's modulus and energy absorption along the three axes of trabecular bone cubes was analysed by non-destructive compression to 0.5% strain using different testing protocols. These protocols included testing with and without pre-conditioning to a viscoelastic steady state, and different orders of test directions. Reproducibility of conditioned tests was generally better than that of non-conditioned tests. No major effect of changing the order of the test direction was found. Three-axial conditioned testing of cubes from the proximal tibial epiphysis of five humans revealed a global transverse isotrophy while most cubes showed orthotropy. The ratio between stiffness along the long axis of the tibia and the stiffness in the transverse plane was 3.7 +/- 0.4 (mean +/- 2 SE). The corresponding ratios for elastic energy storage and viscoelastic energy dissipation were 2.5 +/- 0.2. There was no difference between the relative energy loss during a testing cycle (loss tangent) in the three axes.     

Stiffness behaviour of trabecular bone specimens

Trabecular bone specimens were tested by non-destructive technique with the purpose of investigating stiffness behaviour and optimizing stiffness determination. Cylindrical specimens (n = 25) were loaded repetitively (0.1 Hz, 30 cycles) by axial compression to 50% of predicted ultimate strength and finally compressed to failure. Analyses of single compression curves showed increasing stiffness (E') until a stress level about 50% of ultimate stress followed by decreasing stiffness. Curve fit analysis of the elastic part of the compression curve showed the best fit, when a second order polynomial was used (r = 0.94, p less than 0.001). The stiffness determined non-destructively at the 25% level of ultimate strength increased significantly to the tenth loading cycle followed by a steady state. The precision of stiffness determination as an average of five consecutive measurements at steady state was E' +/- less than 5% (95% confidence limits). A reproducibility test by repetition of the test sequence after 3 h rest showed qualitatively the same stiffness behaviour. The variation of stiffness determination between the two test sequences was +/- 27% at the first loading cycle falling to +/- 12% at steady state.     

Stress relaxation behaviour of trabecular bone specimens

The present study defines several conditions under which stress relaxation tests can be performed and investigates the viscoelastic behaviour of trabecular bone in compression through a series of stress relaxation tests at three strain levels and in three loading directions of each cubic specimen. A visoelastic model is proposed to characterize the behaviour of trabecular bone and a spectrum of relaxation times is determined. Trabecular bone from the femoral head is non-linearly viscoelastic and displays anisotropic behaviour, which cannot be more symmetric elastically than orthotropic.     

A gamma-ray computed tomography scanner for the quantitative measurement of bone density

A special purpose gamma-ray computed tomography scanner has been developed for the precise measurement of bone density in the distal forearm. Details of the scanner hardware and computer analysis technique are given. Suitable phantoms have been used to test the operation of the scanner, which has been used to measure trabecular and cortical bone density with a precision better than 1%.     

Biaxial failure behavior of bovine tibial trabecular bone

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.     

The mechanical properties of human tibial trabecular bone as a function of metaphyseal location

Experimental determination of the elastic modulus and ultimate strength of human tibial trabecular bone as a function of metaphyseal location is presented.

A 1 cm cubic matrix with planes parallel to the subchondral plate was defined on five fresh frozen cadaver tibias. Approximately 400, 7 mm × 10 mm cylindrical bone plugs were cut from the locations defined by the matrix and tested in uniaxial compressive stress at a strain rate of 0.1%s⁻¹. Results of the study indicate that the trabecular bone properties vary as much as two orders of magnitude from one location to another. As might be predicted from Wolff's law, and noted by previous investigators, concentrations of strength arise from the medial and lateral metaphyseal cortices toward the major medial and lateral contact regions.

These results may be valuable for improved analytical modeling and optimal prosthetic design.     

Peripheral quantitative computed tomography of the proximal radius in young subjects--new reference data and interpretation of results

The aim of this contribution is to provide reference data for peripheral quantitative computed tomography (Stratec XCT2000) performed at the proximal radius (the so-called '65% site') of young subjects and to discuss the interpretation of such analyses. Data from a previous reference data study on 469 subjects between 6 and 40 years were re-analyzed and smooth curves were fitted. The corresponding equations allow for calculation of age-, height- and sex-specific z-scores of total cross-sectional area, cortical cross-sectional area, bone mineral content, cortical bone mineral density, total bone mineral density, Strength-Strain Index, muscle cross-sectional area and the ratio between bone mineral content and muscle cross-sectional area. These data should facilitate the clinical use of peripheral quantitative computed tomography in young subjects.     

Erratum to: Mechanical properties of femoral trabecular bone in dogs

After the publication of this work [1], we became aware of the fact that the frequency of the ultrasound transmitter that we used for determining the elastic moduli of the trabecular bone specimens was not correctly specified. The oscillation frequency of the ultrasound transmitter was 2 MHz (and not 100 MHz as stated in our work) while we used a sampling rate of 100 MHz. In our publication, the oscillation frequency and sampling rate were confounded. Therefore also the statement in the discussion that we might have determined elastic moduli of trabecular bone tissue rather than the elastic properties of whole specimens because we used an ultrasound frequency > 2 MHz is wrong and has to be omitted.     

Detection of trabecular bone microdamage by micro-computed tomography

Microdamage is an important component of bone quality and affects bone remodeling. Improved techniques to assess microdamage without the need for histological sectioning would provide insight into the role of microdamage in trabecular bone strength by allowing the spatial distribution of damage within the trabecular microstructure to be measured. Nineteen cylindrical trabecular bone specimens were prepared and assigned to two groups. The specimens in group I were damaged to 3% compressive strain and labeled with BaSO(4). Group II was not loaded, but was labeled with BaSO(4). Micro-computed tomography (Micro-CT) images of the specimens were obtained at 10 microm resolution. The median intensity of the treated bone tissue was compared between groups. Thresholding was also used to measure the damaged area fraction in the micro-CT scans. The histologically measured damaged area fraction, the median CT intensity, and the micro-CT measured damaged area fraction were all higher in the loaded group than in the unloaded group, indicating that the micro-CT images could differentiate the damaged specimen group from the unloaded specimens. The histologically measured damaged area fraction was positively correlated with the micro-CT measured damaged area fraction and with the median CT intensity of the bone, indicating that the micro-CT images can detect microdamage in trabecular bone with sufficient accuracy to differentiate damage levels between samples. This technique provides a means to non-invasively assess the three-dimensional distribution of microdamage within trabecular bone test specimens and could be used to gain insight into the role of trabecular architecture in microdamage formation.     

Influence of physical activity on tibial bone material properties in laying hens

Laying hens develop a type of osteoporosis that arises from a loss of structural bone, resulting in high incidence of fractures. In this study, a comparison of bone material properties was made for lines of hens created by divergent selection to have high and low bone strength and housed in either individual cages, with restricted mobility, or in an aviary system, with opportunity for increased mobility. Improvement of bone biomechanics in the high line hens and in aviary housing was mainly due to increased bone mass, thicker cortical bone and more medullary bone. However, bone material properties such as cortical and medullary bone mineral composition and crystallinity as well as collagen maturity did not differ between lines. However, bone material properties of birds from the different type of housing were markedly different. The cortical bone in aviary birds had a lower degree of mineralization and bone mineral was less mature and less organized than in caged birds. These differences can be explained by increased bone turnover rates due to the higher physical activity of aviary birds that stimulates bone formation and bone remodeling. Multivariate statistical analyses shows that both cortical and medullary bone contribute to breaking strengthThe cortical thickness was the single most important contributor while its degree of mineralization and porosity had a smaller contribution. Bone properties had poorer correlations with mechanical properties in cage birds than in aviary birds presumably due to the greater number of structural defects of cortical bone in cage birds.     

Preparation of on-axis cylindrical trabecular bone specimens using micro-CT imaging

The Orientation of trabecular bone specimens for mechanical testing must be carefully controlled. A method for accurately preparing on-axis cylindrical specimens using high-resolution micro-CT imaging was developed. Sixteen cylindrical specimens were prepared from eight bovine tibiae. High-resolution finite element models were generated from micro-CT images of parallelepipeds and used to determine the principal material coordinate system of each parallelepiped. A cylindrical specimen was then machined with a diamond coring bit. The resulting specimens were scanned again to evaluate the orientation. The average deviation between the principal fabric orientation and the longitudinal axis of the cylindrical specimen was only 4.70 +/- 3.11 degrees.     

The effect of constraint on the mechanical behaviour of trabecular bone specimens

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).     

High energy X-ray scattering tomography applied to bone

High energy synchrotron X-ray scattering was developed for reconstruction of specimen cross-sections. The technique was applied to a model specimen of cortical bone containing a capillary tube of silicon, and reconstructions were produced with either full diffraction rings or texture-related subsets of a given ring. The carbonated apatite (cAp) 00.2 and 22.2 reconstructions and the Si 311 reconstructions agreed with absorption-based reconstructions from the measured X-ray transmissivity recorded during diffraction pattern acquisition and from reconstructions produced subsequently of the same specimen using a commercial microCT (microComputed Tomography) scanner.     

Opportunities for biomineralization research using multiscale computed X-ray tomography as exemplified by bone imaging

Biominerals typically have complex hierarchical structures traversing many length scales. This makes their structural characterization complicated, since it requires 3D techniques that can probe full specimens at down to nanometer-resolution, a combination that is difficult – if not impossible – to achieve simultaneously. One challenging example is bone, a mineralized tissue with a highly complex architecture that is replete with a network of cells. X-ray computed tomography techniques enable multiscale structural characterization through the combination of various equipment and emerge as promising tools for characterizing biominerals. Using bone as an example, we discuss how combining different X-ray imaging instruments allow characterizing bone structures from the nano- to the organ-scale. In particular, we compare and contrast human and rodent bone, emphasize the importance of the osteocyte lacuno-canalicular network in bone, and finally illustrate how combining synchrotron X-ray imaging with laboratory instrumentation for computed tomography is especially helpful for multiscale characterization of biominerals.     

First application of X-ray refraction-based computed tomography to a biomedical object

We have developed X-ray refraction-based computed tomography (CT) that is able to visualize soft tissue in between hard tissue. The experimental system consists of Si(220) diffraction double-crystals and is called the DEI (diffraction-enhanced imaging) method, in which the object is located between the crystals and a CCD camera to acquire data as 360 X-ray images. The X-ray energy used was 17.5 keV. The algorithm used to reconstruct CT images was developed by A. Maksimenko and colleagues. We successfully visualized articular cartilage and the distribution of bone marrow, which are inner structures. Our method has much higher contrast compared to the conventional absorption-based CT system.     

Interrelationship of trabecular mechanical and microstructural properties in sheep trabecular bone

The ability to evaluate fracture risk at an early time point is essential for improved prognostics as well as enhanced treatment in cases of bone loss such as from osteoporosis. Improving the diagnostic ability is inherent upon both high-resolution non-invasive imaging, and a thorough understanding of how the derived indices of structure and density relate to its true mechanical behavior. Using sheep femoral trabecular bone with a range of strength, the interrelationship of mechanical and microstructural parameters was analyzed using multi-directional mechanical testing and micro-computed tomography. Forty-five cubic trabecular bone samples were harvested from 23 adult female sheep, some of whom had received hind-limb vibratory stimuli over the course of 2 years with consequently enhanced mechanical properties. These samples were pooled into a low, medium, or high strength group for further analysis. The findings show that microCT indices that are structural in nature, e.g., structural model index (SMI) (r2=0.85, p<0.0001) is as good as more density oriented indices like bone volume/total volume (BV/TV) (r2=0.81, p<0.0001) in predicting the ultimate strength of a region of trabecular bone. Additionally, those indices more related to global changes in trabecular structure such as connectivity density (ConnD) or degree of anisotropy (DA) are less able to predict the mechanical properties of bone. Interrelationships of trabecular indices such as trabecular number (TbN), thickness (TbTh), and spacing (TbSp) provide clues as to how the trabecular bone will remodel to ultimately achieve differences in the apparent mechanical properties. For instance, the analysis showed that a loss of bone primarily affects the connectedness and overall number of trabeculae, while increased strength results in an increase of the overall thickness of trabeculae while not improving the connectedness. Certainly, the microCT indices studied are able to predict the bulk mechanical properties of a trabecular ROI well, leaving unaccounted only about 15-20% of its inherent variability. Diagnostically, this implies that future work on the early prediction of fracture risk should continue to explore the role of bone quality as the key factors or as an adjuvant to bone quantity (e.g., apparent density).     

Effects of damage on the orthotropic material symmetry of bovine tibial trabecular bone

The macroscopic mechanical properties of trabecular bone can be predicted by its architecture using theoretical relationships between the elastic and architectural properties. Microdamage caused by overloading or fatigue decreases the apparent elastic moduli of trabecular bone requiring these relationships to be modified to predict the damaged elastic properties. In the case of isotropic damage, the apparent level elastic properties could be determined by multiplying all of the elastic constants by a single scalar factor. If the damage is anisotropic, the elastic constants may change by differing factors and the material coordinate system could become misaligned with the fabric coordinate system. High-resolution finite element models were used to simulate damage overloading on seven trabecular bone specimens subjected to pure shear strain in two planes. Comparison of the apparent elastic moduli of the specimens before and after damage showed that the reduction of the elastic moduli was anisotropic. This suggests that the microdamage within the specimens was inhomogeneous. However, after damage the specimens exhibited nearly orthotropic material symmetry as they did before damage. Changes in the orientation of the orthotropic material coordinate system were also small and occurred primarily in the transverse plane. Thus, while damage in trabecular bone is anisotropic, the material coordinate system remains aligned with the fabric tensor.