Dependence of mechanical properties of trabecular bone on plate–rod microstructure determined by individual trabecula segmentation (ITS)

Individual trabecula segmentation (ITS) technique can decompose the trabecular bone network into individual trabecular plates and rods and is capable of quantifying the plate/rod-related microstructural characteristics of trabecular bone. This novel technique has been shown to be able to provide in-depth insights into micromechanics and failure mechanisms of human trabecular bone, as well as to distinguish the fracture status independent of area bone mineral density in clinical applications. However, the plate/rod microstructural parameters from ITS have never been correlated to experimentally determined mechanical properties of human trabecular bone. In this study, on-axis cylindrical trabecular bone samples from human proximal tibia (n=22), vertebral body (n=10), and proximal femur (n=21) were harvested, prepared, scanned using micro computed-tomography (µCT), analyzed with ITS and mechanically tested. Regression analyses showed that the plate bone volume fraction (pBV/TV) and axial bone volume fraction (aBV/TV) calculated by ITS analysis correlated the best with elastic modulus (R²=0.96–0.97) and yield strength (R²=0.95–0.96). Trabecular plate-related microstructural parameters correlated highly with elastic modulus and yield strength, while most rod-related parameters were found inversely and only moderately correlated with the mechanical properties. In addition, ITS analysis also identified that trabecular bone at human femoral neck had the highest trabecular plate-related parameters while the other sites were similar with each other in terms of plate–rod microstructure.     

Analysis of microstructural and mechanical alterations of trabecular bone in a simulated three-dimensional remodeling process

Bone remodeling is a complex dynamic process, which modulates both bone mass and bone microstructure. In addition to bone mass, bone microstructure is an important contributor to bone quality in osteoporosis and fragility fractures. However, the quantitative knowledge of evolution of three-dimensional (3D) trabecular microstructure in adaptation to the external forces is currently limited. In this study, a new 3D simulation method of remodeling of human trabecular bone was developed to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to different external loading conditions. The morphological features of trabecular plate and rod, such as thickness and number density in different orientations were monitored during the remodeling process using a novel imaging analysis technique, namely Individual Trabecula Segmentation (ITS). We showed that the volume fraction and microstructures of trabecular bone including, trabecular type and orientation, were determined by the applied mechanical load. Particularly, the morphological parameters of trabecular plates were more sensitive to the applied load, indicating that they played the major role in the mechanical properties of the trabecular bone. Reducing the applied load caused severe microstructural deteriorations of trabecular bone, such as trabecular plate perforation, rod breakage, and a conversion from plates to rods.     

Application of homogenization theory to the study of trabecular bone mechanics.

It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hypothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and/or strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region, (R2 greater than 0.5 for proximal humerus specimens, R2 less than 0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV/TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at 10-20% BV/TV.     

Comparison of HR-pQCT- and microCT-based finite element models for the estimation of the mechanical properties of the calcaneus trabecular bone

The calcaneus bone is formed of extensive trabecular bone and is therefore well suited to be used as an example of loaded bone to establish the ability of combining microfinite element (microFE) technique with high-resolution peripheral quantitative computed tomography (HR-pQCT) in determining its mechanical properties. HR-pQCT is increasingly used as a tool for in vivo bone clinical research, but its use has been limited to the distal radius and tibia. The goal of this study was to determine the applicability of HR-pQCT-derived microFE models of the calcaneus trabecular bone with 82 μm voxel size with reference to higher-resolution microCT-based models taken as gold standard. By comparing the outputs of microFE models generated from both HR-pQCT and microCT images of the trabecular bone of five calcaneus cadaveric specimens, it was found that the HR-pQCT-based models predicted mechanical properties for fracture load, total reaction force and von Mises stress are considerably different from microCT-based counterparts by 33, 64 and 70%, respectively. Also, the morphological analysis showed a comprehensive geometrical difference between HR-pQCT-based microFE models and their microCT-based equivalents. The results of the HR-pQCT-based models were found to have strong dependency on the threshold value chosen to binarise the images prior to finite element modelling. In addition, it was found that the voxel size has a strong impact on accuracy of imaged-based microFE models compared to other factors such as the presence of soft tissue and image scanning integration time. Therefore, although HR-pQCT has shown to be useful to predict overall structural and biomechanical changes, it is limited in providing local accurate biomechanical properties of trabecular bone and therefore should be used with caution when assessing bone remodelling through local changes of trabecular bone apposition and resorption in disease treatment monitoring.     

On the influence of mechanical conditions in osteochondral defect healing

Despite the introduction of new surgical techniques, the treatment of cartilage defects remains challenging. Delay or complete failure of cartilage healing is associated with problems in biological regeneration. The influence of mechanical conditions on this process, however, remains unevaluated. Osteochondral defects were generated on the left femoral condyle in 18 Yucatan minipigs. After 4, 6 and 12 weeks the defect filling, trabecular orientation and bone density were compared to the intact contralateral side. The mechanical straining during this period was then analyzed using an adaptive finite element technique. Histologically, the osteochondral defects showed bone resorption at the base and bone formation from the circumference. At 12 weeks, the macroscopically healed specimens showed fibrous cartilage formation, a minimally organized trabecular structure and increased trabecular volume fraction compared to the controls (p < 0.002). The amount of cancellous, cartilagineous, and fibrous tissue and the defect size as measured in histomorphometric analysis for the three time points (4, 6 and 12 weeks) was comparable in magnitude to that predicted by finite element analysis. The simulated osteochondral healing process was not fully capable of re-establishing a hyaline-like cartilage layer. The correlation between simulation and histology allows identification of mechanical factors that appear to have a larger impact on the healing of osteochondral defects than previously considered.     

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.     

Trabecular architecture in the humeral metaphyses of non-avian reptiles (Crocodylia,Squamata and Testudines): Lifestyle,allometry and phylogeny

The lifestyle of extinct tetrapods is often difficult to assess when clear morphological adaptations such as swimming paddles are absent. According to the hypothesis of bone functional adaptation, the architecture of trabecular bone adapts sensitively to physiological loadings. Previous studies have already shown a clear relation between trabecular architecture and locomotor behavior, mainly in mammals and birds. However, a link between trabecular architecture and lifestyle has rarely been examined. Here, we analyzed trabecular architecture of different clades of reptiles characterized by a wide range of lifestyles (aquatic, amphibious, generalist terrestrial, fossorial, and climbing). Humeri of squamates, turtles, and crocodylians have been scanned with microcomputed tomography. We selected spherical volumes of interest centered in the proximal metaphyses and measured trabecular spacing, thickness and number, degree of anisotropy, average branch length, bone volume fraction, bone surface density, and connectivity density. Only bone volume fraction showed a significant phylogenetic signal and its significant difference between squamates and other reptiles could be linked to their physiologies. We found negative allometric relationships for trabecular thickness and spacing, positive allometries for connectivity density and trabecular number and no dependence with size for degree of anisotropy and bone volume fraction. The different lifestyles are well separated in the morphological space using linear discriminant analyses, but a cross-validation procedure indicated a limited predictive ability of the model. The trabecular bone anisotropy has shown a gradient in turtles and in squamates: higher values in amphibious than terrestrial taxa. These allometric scalings, previously emphasized in mammals and birds, seem to be valid for all amniotes. Discriminant analysis has offered, to some extent, a distinction of lifestyles, which however remains difficult to strictly discriminate. Trabecular architecture seems to be a promising tool to infer lifestyle of extinct tetrapods, especially those involved in the terrestrialization.     

Synchrotron radiation micro-CT at the micrometer scale for the analysis of the three-dimensional morphology of microcracks in human trabecular bone

Bone quality is an important concept to explain bone fragility in addition to bone mass. Among bone quality factors, microdamage which appears in daily life is thought to have a marked impact on bone strength and plays a major role in the repair process. The starting point for all studies designed to further our understanding of how bone microdamage initiate or dissipate energy, or to investigate the impact of age, gender or disease, remains reliable observation and measurement of microdamage. In this study, 3D Synchrotron Radiation (SR) micro-CT at the micrometric scale was coupled to image analysis for the three-dimensional characterization of bone microdamage in human trabecular bone specimens taken from femoral heads. Specimens were imaged by 3D SR micro-CT with a voxel size of 1.4 μm. A new tailored 3D image analysis technique was developed to segment and quantify microcracks. Microcracks from human trabecular bone were observed in different tomographic sections as well as from 3D renderings. New 3D quantitative measurements on the microcrack density and morphology are reported on five specimens. The 3D microcrack density was found between 3.1 and 9.4/mm3 corresponding to a 2D density between 0.55 and 0.76 /mm2. The microcrack length and width measured in 3D on five selected microcrack ranged respectively from 164 μm to 209 μm and 100 μm to 120 μm. This is the first time that various microcracks in unloaded human trabecular bone--from the simplest linear crack to more complex cross-hatch cracks--have been examined and quantified by 3D imaging at this scale. The suspected complex morphology of microcracks is here considerably more evident than in the 2D observations. In conclusion, this technique opens new perspective for the 3D investigation of microcracks and the impact of age, disease or treatment.     

Computational simulation of trabecular adaptation progress in human proximal femur during growth

There are a large number of clinical and experimental studies that analyzed trabecular architecture as a result of bone adaptation. However, only a limited amount of quantitative data is currently available on the progress of trabecular adaptation during growth. In this paper, we proposed a two-step numerical simulation method that predicts trabecular adaptation progress during growth using a recently developed topology optimization algorithm, design space optimization (DSO), under the hypothesis that the mechanisms of DSO are functionally equivalent to those of bone adaptation. We applied the proposed scheme to trabecular adaptation simulation in human proximal femur. For the simulation, the full trabecular architecture in human proximal femur was represented by a two-dimensional μFE model with 50 μm resolution. In Step 1, we determined a reference value that regulates trabecular adaptation in human proximal femur. In Step 2, we simulated trabecular adaptation in human proximal femur during growth with the reference value derived in Step 1. We analyzed the architectural and mechanical properties of trabecular patterns through iterations. From the comparison with experimental data in the literature, we showed that in the early growth stage trabecular adaptation was achieved mainly by increasing bone volume fraction (or trabecular thickness), while in the later stage of the development the trabecular architecture gained higher structural efficiency by increasing structural anisotropy with a relatively low level of bone volume fraction (or trabecular thickness). We demonstrated that the proposed numerical framework predicted the growing progress of trabecular bone that has a close correlation with experimental data.     

Long-term dose response of trabecular bone in mice to proton radiation

Astronauts on exploratory missions will experience a complex environment, including microgravity and radiation. While the deleterious effects of unloading on bone are well established, fewer studies have focused on the effects of radiation. We previously demonstrated that 2 Gy of ionizing radiation has deleterious effects on trabecular bone in mice 4 months after exposure. The present study investigated the skeletal response after total doses of proton radiation that astronauts may be exposed to during a solar particle event. We exposed mice to 0.5, 1 or 2 Gy of whole-body proton radiation and killed them humanely 117 days later. Tibiae and femora were analyzed using microcomputed tomography, mechanical testing, mineral composition and quantitative histomorphometry. Relative to control mice, mice exposed to 2 Gy had significant differences in trabecular bone volume fraction (-20%), trabecular separation (+11%), and trabecular volumetric bone mineral density (-19%). Exposure to 1 Gy radiation induced a nonsignificant trend in trabecular bone volume fraction (-13%), while exposure to 0.5 Gy resulted in no differences. No response was detected in cortical bone. Further analysis of the 1-Gy mice using synchrotron microCT revealed a significantly lower trabecular bone volume fraction (-13%) than in control mice. Trabecular bone loss 4 months after exposure to 1 Gy highlights the importance of further examination of how space radiation affects bone.     

Testing two predictions for fracture load using computer models of trabecular bone

Aging induces several types of architectural changes in trabecular bone including thinning, increased levels of anisotropy, and perforation. It has been determined, on the basis of analysis of mathematical models, that reduction in fracture load caused by perforation is significantly higher than those due to equivalent levels of thinning or anisotropy. The analysis has also provided an expression which relates the fractional reduction of strength tau to the fraction of elements nu that have been removed from a network. Further, it was proposed that the ratio Gamma of the elastic constant of a sample and its linear response at resonance can be used as a surrogate for tau. Experimental validation of these predictions requires following architectural changes in a given sample of trabecular bone; techniques to study such changes using microcomputed tomography are only beginning to be available. In the present study, we use anatomically accurate computer models constructed from digitized images of bone samples for the purpose. Images of healthy bone are subjected to successive levels of synthetic degradation via surface erosion. Computer models constructed from these images are used to calculate their fracture load and other mechanical properties. Results from these computations are shown to be consistent with predictions derived from the analysis of mathematical models. Although the form of tau(nu) is known, parameters in the expression are expected to be sample-specific, and hence nu is not a reliable predictor of strength. We provide an example to demonstrate this. In contrast, analysis of model networks shows that the linear part of tau(Gamma) depends only on the structure of trabecular bone. Computations on models constructed from samples of iliac crest trabecular bone are shown to be in agreement with this assertion. Since Gamma can be computed from a vibrational assessment of bone, we argue that the latter can be used to introduce new surrogates for bone strength and hence diagnostic tools for osteoporosis.     

Patterns in ontogeny of human trabecular bone from SunWatch Village in the Prehistoric Ohio Valley: general features of microarchitectural change

Although adult skeletal morphological variation is best understood within the framework of age-related processes, relatively little research has been directed towards the structure of and variation in trabecular bone during ontogeny. We report here new quantitative and structural data on trabecular bone microarchitecture in the proximal tibia during growth and development, as demonstrated in a subadult archaeological skeletal sample from the Late Prehistoric Ohio Valley. These data characterize the temporal sequence and variation in trabecular bone structure and structural parameters during ontogeny as related to the acquisition of normal functional activities and changing body mass. The skeletal sample from the Fort Ancient Period site of SunWatch Village is composed of 33 subadult and three young adult proximal tibiae. Nondestructive microCT scanning of the proximal metaphyseal and epiphyseal tibia captures the microarchitectural trabecular structure, allowing quantitative structural analyses measuring bone volume fraction, degree of anisotropy, trabecular thickness, and trabecular number. The microCT resolution effects on structural parameters were analyzed. Bone volume fraction and degree of anisotropy are highest at birth, decreasing to low values at 1 year of age, and then gradually increasing to the adult range around 6-8 years of age. Trabecular number is highest at birth and lowest at skeletal maturity; trabecular thickness is lowest at birth and highest at skeletal maturity. The results of this study highlight the dynamic sequential relationships between growth/development, general functional activities, and trabecular distribution and architecture, providing a reference for comparative studies.     

A Non-Destructive Method for Distinguishing Reindeer Antler (Rangifer tarandus) from Red Deer Antler (Cervus elaphus) Using X-Ray Micro-Tomography Coupled with SVM Classifiers

Over the last decade, biomedical 3D-imaging tools have gained widespread use in the analysis of prehistoric bone artefacts. While initial attempts to characterise the major categories used in osseous industry (i.e. bone, antler, and dentine/ivory) have been successful, the taxonomic determination of prehistoric artefacts remains to be investigated. The distinction between reindeer and red deer antler can be challenging, particularly in cases of anthropic and/or taphonomic modifications. In addition to the range of destructive physicochemical identification methods available (mass spectrometry, isotopic ratio, and DNA analysis), X-ray micro-tomography (micro-CT) provides convincing non-destructive 3D images and analyses. This paper presents the experimental protocol (sample scans, image processing, and statistical analysis) we have developed in order to identify modern and archaeological antler collections (from Isturitz, France). This original method is based on bone microstructure analysis combined with advanced statistical support vector machine (SVM) classifiers. A combination of six microarchitecture biomarkers (bone volume fraction, trabecular number, trabecular separation, trabecular thickness, trabecular bone pattern factor, and structure model index) were screened using micro-CT in order to characterise internal alveolar structure. Overall, reindeer alveoli presented a tighter mesh than red deer alveoli, and statistical analysis allowed us to distinguish archaeological antler by species with an accuracy of 96%, regardless of anatomical location on the antler. In conclusion, micro-CT combined with SVM classifiers proves to be a promising additional non-destructive method for antler identification, suitable for archaeological artefacts whose degree of human modification and cultural heritage or scientific value has previously made it impossible (tools, ornaments, etc.).     

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

Trabecular plates play an important role in determining elastic moduli of trabecular bone. However, the relative contribution of trabecular plates and rods to strength behavior is still not clear. In this study, individual trabeculae segmentation (ITS) and nonlinear finite element (FE) analyses were used to evaluate the roles of trabecular types and orientations in the failure initiation and progression in human vertebral trabecular bone. Fifteen human vertebral trabecular bone samples were imaged using micro computed tomography (μCT), and segmented using ITS into individual plates and rods by orientation (longitudinal, oblique, and transverse). Nonlinear FE analysis was conducted to perform a compression simulation for each sample up to 1% apparent strain. The apparent and relative trabecular number and tissue fraction of failed trabecular plates and rods were recorded during loading and data were stratified by trabecular orientation. More trabecular rods (both in number and tissue fraction) failed at the initiation of compression (0.1–0.2% apparent strain) while more plates failed around the apparent yield point (>0.7% apparent strain). A significant correlation between plate bone volume fraction (pBV/TV) and apparent yield strength was found (r²=0.85). From 0.3% to 1% apparent strain, significantly more longitudinal trabecular plate and transverse rod failed than other types of trabeculae. While failure initiates at rods and rods fail disproportionally to their number, plates contribute significantly to the apparent yield strength because of their larger number and tissue volume. The relative failed number and tissue fraction at apparent yield point indicate homogeneous local failure in plates and rods of different orientations.     

Effects of thresholding techniques on microCT-based finite element models of trabecular bone

Microimaging based finite element analysis is widely used to predict the mechanical properties of trabecular bone. The choice of thresholding technique, a necessary step in converting grayscale images to finite element models, can significantly influence the predicted bone volume fraction and mechanical properties. Therefore, we investigated the effects of thresholding techniques on microcomputed tomography (micro-CT) based finite element models of trabecular bone. Three types of thresholding techniques were applied to 16-bit micro-CT images of trabecular bone to create three different models per specimen. Bone volume fractions and apparent moduli were predicted and compared to experimental results. In addition, trabecular tissue mechanical parameters and morphological parameters were compared among different models. Our findings suggest that predictions of apparent mechanical properties and structural properties agree well with experimental measurements regardless of the choice of thresholding methods or the format of micro-CT images.     

3D analysis from micro-MRI during in situ compression on cancellous bone

A mini-compression jig was built to perform in situ tests on bovine trabecular bone monitored by micro-MRI. The MRI antenna provided an isotropic resolution of 78 μm that allows for a volume correlation method to be used. Three-dimensional displacement fields are then evaluated within the bone sample during the compression test. The performances of the correlation method are evaluated and discussed to validate the technique on trabecular bone. By considering correlation residuals and estimates of acquisition noise, the measured results are shown to be trustworthy. By analyzing average strain levels for different interrogation volumes along the loading direction, it is shown that the sample size is less than that of a representative volume element. This study shows the feasibility of the 3D-displacement and strain field analyses from micro-MRI images. Other biological tissues could be considered in future work.     

A new approach to quantify trabecular resorption adjacent to cemented knee arthroplasty

A new micro-computed tomography (μCT) image processing approach to estimate the loss of cement-bone interlock was developed using the concept that PMMA cement flows and cures around trabeculae during the total knee arthroplasty procedure. The initial mold shape of PMMA cement was used to estimate the amount of interdigitated bone at the time of implantation and following in vivo service using enbloc human postmortem retrievals. Laboratory prepared specimens, where there would be no biological bone resorption, were used as controls to validate the approach and estimate errors. The image processing technique consisted of identifying bone and cement from the μCT scan set, dilation of the cement to identify the cement cavity space, and Boolean operations to identify the different components of the interdigitated cement-bone regions. For laboratory prepared specimens, there were small errors in the estimated resorbed bone volume fraction (reBVfr=0.11 ± 0.09) and loss in contact area fraction (CAfr=0.06 ± 0.15). These values would be zero if there were no error in the method. For the postmortem specimens, the resorbed volume fraction (reBVfr=0.85 ± 0.16) was large, meaning that only 15% of the cement mold shape was still filled with bone. The loss of contact area fraction (CAfr=0.84 ± 0.17) was similarly large. This new approach provides a convenient method to visualize and quantify trabecular bone loss from interdigitated regions from postmortem retrievals. The technique also illustrates for the first time that there are dramatic changes in how bone is fixed to cement following in vivo service.     

Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone

Strain measurement is an essential tool in the study of trabecular bone structure-function relationships. Digital volume correlation (DVC) is a measurement technique that quantifies strains throughout the interior of a specimen, rather than simply those on the surface. DVC relies on tracking the movement of microstructural features, and as such, the accuracy and precision of this technique may depend on trabecular structure. This study quantified displacement and strain measurement errors in six types of trabecular bone that spanned a wide range of volume fraction and trabecular architecture. Accuracy and precision were compared across bone type and also across three DVC methods. Both simulated and real displacement fields were analyzed using micro-computed tomography images of specimens from the bovine distal femur, bovine proximal tibia, rabbit distal femur, rabbit proximal tibia, rabbit vertebra, and human vertebra. Differences as large as three-fold in accuracy and precision of the displacements and strains were found among DVC methods and among bone types. The displacement precision and the strain accuracy and precision were correlated with measures of trabecular structure such as structural model index. These results demonstrate that the performance of the DVC technique can depend on trabecular structure. Across all bone types, the displacement and strain errors ranged 1.86-3.39 microm and 345-794 microepsilon, respectively. For specimens from the human vertebra and bovine distal femur, the measurement errors were approximately 20 times smaller than the yield strain. In these cases, DVC is a viable technique for measuring pre- and post-yield strains throughout trabecular bone specimens and the trabecular compartment of whole bones.     

Quantification of trabecular bone microdamage using the virtual internal bond model and the individual trabeculae segmentation technique

Trabecular bone microdamage significantly influences the skeletal integrity and bone remodelling process. In this paper a novel constitutive model, called the virtual internal bond model (VIB), was adopted for simulating the damage behaviour of bone tissue. A unique 3D image analysis technique, named individual trabeculae segmentation, was used to analyse the effects of microarchitectures on the damage behaviours of trabecular bone. We demonstrated that the process of initiation and accumulation of microdamage in trabecular bone samples can be captured by the VIB-embedded finite-element method simulation without a separate fracture criterion. Our simulation results showed that the microdamage can occur at as early as about 0.2–0.4% apparent strain, and a large volume of microdamage was accumulated around the apparent yield strain. In addition we found that the plate-like trabeculae, especially the longitudinal ones, take crucial roles in the microdamage behaviours of trabecular bone.     

A New Computational Efficient Approach for Trabecular Bone Analysis using Beam Models Generated with Skeletonized Graph Technique

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-Line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone.