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.     

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.     

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.     

Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques

In this study, we investigate if finite element (FE) analyses of human trabecular bone architecture based on 168 μm images can provide relevant information about the bone mechanical characteristics. Three human trabecular bone samples, one taken from the femoral head, one from the iliac crest, and one from the lumbar spine, were imaged with micro-computed tomography (micro-CT) using a 28 μm resolution. After reconstruction the resolution was coarsened to 168 μm. First, all reconstructions were thresholded and directly converted to FE-models built of hexahedral elements. For the coarser resolutions of two samples, this resulted in a loss of trabecular connections and a subsequent loss of stiffness. To reduce this effect, a tetrahedral element meshing based on the marching cubes algorithm, as well as a modified hexahedron meshing, which thresholds the image such that load carrying bone mass is preserved, were employed. For each sample elastic moduli and tissue Von Mises stresses of the three different 168 μm models were compared to those from the hexahedron 28 μm model. For one sample the hexahedron meshing at 168 μm produced excellent results. For the other two samples the results obtained from the hexahedral models at 168 μm resolution were poor. Considerably better results were attained for these samples when using the mass-compensated or tetrahedron meshing techniques. We conclude that the accuracy of the FE-models at 168 μm strongly depends on the bone morphology, in particular its trabecular thickness. A substantial loss of trabecular connections during the hexahedron meshing process indicates that poor FE results will be obtained. In this case the tetrahedron or mass-compensated hexahedron meshing techniques can reduce the loss of connections and produce better results than the plain hexahedron meshing techniques.     

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load–displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R² = 0.53–0.65, average error of 13–17%). A lower correlation was found for failure load (R² = 0.21–0.48, average error of 9–15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R² = 0.75–0.80 for stiffness, R² = 0.55–0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

     

Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation

Assessment of the mechanical properties of trabecular bone is of major biological and clinical importance for the investigation of bone diseases, fractures and their treatments. Finite element (FE) methods are getting increasingly popular for quantifying the elastic and failure properties of trabecular bone. In particular, voxel-based FE methods have been previously used to calculate the effective elastic properties of trabecular microstructures. However, in most studies, bone tissue moduli were assumed or back-calculated to match the apparent elastic moduli from experiments, which often lead to surprisingly low values when compared to nanoindentation results. In this study, voxel-based FE analysis of trabecular bone is combined with physical measures of volume fraction, micro-CT (microCT) reconstructions, uniaxial mechanical tests and specimen-specific nanoindentation tests for proper validation of the method. Cylindrical specimens of cancellous bone were extracted from human femurs and their volume fraction determined with Archimede's method. Uniaxial apparent modulus of the specimens was measured with an improved tension-compression testing protocol that minimizes boundary artefacts. Their microCT reconstructions were segmented to match the measured bone volume fraction and used to create full-size voxel models with 30-45 microm element size. For each specimen, linear isotropic elastic material properties were defined based on specific nanoindentation measurements of its embedded bone tissue. Linear FE analyses were finally performed to simulate the uniaxial mechanical tests. Additional parametric analyses were performed to evaluate the potential errors on the predicted apparent modulus arising from variations in segmentation threshold, tissue modulus, and the use of 125-mm(3) cubic sub-regions. The results demonstrate an excellent correspondence between experimental measures and FE predictions of uniaxial apparent modulus. In conclusion, the adopted voxel-based FE approach is found to be a robust method to predict the linear elastic properties of human cancellous bone, provided segmentation of the microCT reconstructions is carefully calibrated, tissue modulus is known a priori and the entire region of interest is included in the analysis.     

Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties

High-resolution voxel-based finite element software, such as FEEBE developed at the NCBES, is widely used for studying trabecular bone at the micro-scale. A new approach to determine heterogeneous bone tissue material properties for computational models was proposed in this study. The specimen-specific range of tissue moduli across strut width was determined from nanoindentation testing. This range was mapped directly using linear interpolation to that specimen's micro-computed tomography (microCT) grey value range as input material properties for finite element analysis. The method was applied to cuboid trabecular bone samples taken from eight, 4-year-old (skeletally mature) ovine L5 vertebrae. Before undergoing experimental uniaxial compression tests, the samples were microCT scanned and 30 microm resolution finite element models were generated. The linear elastic finite element models were compressed to 1% strain. This material property assignment method for computational models accurately reproduced the experimentally determined apparent modulus and concentrations of stress at locations of failure.     

The effects of bone and pore volume fraction on the mechanical properties of PMMA/bone biopsies extracted from augmented vertebrae

Vertebroplasty forms a porous PMMA/bone composite which was shown to be weaker and less stiff than pure PMMA. It is not known what determines the mechanical properties of such composites in detail. This study investigated the effects of bone volume fraction (BV/TV), cement porosity (PV/(TV-BV), PV…pore volume) and cement stiffness. Nine human vertebral bodies were augmented with either standard or low-modulus PMMA cement and scanned with a HR-pQCT system before and after augmentation. Fourteen cylindrical PMMA/bone biopsies were extracted from the augmented region, scanned with a micro-CT system and tested in compression until failure. Micro-finite element (FE) models of the complete biopsies, of the trabecular bone alone as well as of the porous cement alone were generated from CT images to gain more insight into the role of bone and pores. PV/(TV-BV) and experimental moduli of standard/low-modulus cement (R(2)=0.91/0.98) as well as PV/(TV-BV) and yield stresses (R(2)=0.92/0.83) were highly correlated. No correlation between BV/TV (ranging from 0.057 to 0.138) and elastic moduli was observed (R(2)< 0.05). Interestingly, the micro-FE models of the porous cement alone reproduced the experimental elastic moduli of the standard/low-modulus cement biopsies (R(2)=0.75/0.76) more accurately than the models with bone (R(2)=0.58/0.31). In conclusion, the mechanical properties of the biopsies were mainly determined by the cement porosity and the cement material properties. The study showed that bone tissue inside the biopsies was mechanically "switched off" such that load was carried essentially by the porous PMMA.     

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.     

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.     

Three-dimensional analysis of nonhuman primate trabecular architecture using micro-computed tomography

Until recently, detailed analyses of the architecture of nonhuman primate cancellous bone have not been possible due to a combination of methodological constraints, including poor resolution imaging or destructive protocols. The development of micro-computed tomography (microCT) and morphometric methods associated with this imaging modality offers anthropologists a new means to study the comparative architecture of cancellous bone. Specifically, microCT will allow anthropologists to investigate the relationship between locomotor behavior and trabecular structure. We conducted a preliminary study on the trabecular patterns in the proximal humerus and femur of Hylobates lar, Ateles paniscus, Macaca mulatta, and Papio anubis to investigate the quantitative differences in their trabecular architecture and evaluate the potential of microCT in anthropological inquiry. MicroCT allows the researcher to evaluate variables beyond simple two-dimensional orientations and radiographic densities. For example, this methodology facilitates the study of trabecular thickness and bone volume fraction using three-dimensional data. Results suggest that density-related parameters do not reliably differentiate suspensory-climbing species from quadrupedal species. However, preliminary results indicate that measurements of the degree of anisotropy, a measure of trabecular orientation uniformity, do distinguish suspensory-climbing taxa from more quadrupedal species. The microCT method is an advance over conventional radiography and medical CT because it can accurately resolve micron-sized struts that make up cancellous bone, and from these images a wide array of parameters that have been demonstrated to be related to cancellous bone mechanical properties can be measured. Methodological problems pertinent to any comparative microCT study of primate trabecular architecture are discussed.     

Micro CT and Micro MR imaging of 3D architecture of animal skeleton

Quantitative assessment of three-dimensional (3D) trabecular structural characteristics may improve our ability to understand the pathophysiology of osteoporosis, to test the efficacy of pharmaceutical intervention, and to estimate bone biomechanical properties. Considerable progress has been made in advanced imaging techniques for noninvasive and/or nondestructive assessment of 3D trabecular structure and connectivity. Micro computed tomography (microCT) has been used to measure 3D trabecular bone structure in rats, both in vivo and in vitro. It can directly quantify 3D trabecular bone structure such as trabecular volume, trabecular thickness, number, separation, structure model index, degree of anisotropy, and connectivity, in a model-independent manner. We have used microCT to study ovariectomy (OVX) induced osteopenia in rats and its treatment with agents such as estrogen, and sodium fluoride. We have demonstrated that 3D microCT can quantify mouse trabecular and cortical bone structure with an isotropic resolution of 9 microm(3). It is also useful for studying osteoporosis in mice and in phenotypes of transgenic mice or gene knockout mice. MicroCT can be used to quantify osteogenesis in mouse Ilizarov leg lengthening procedures, to quantify osteoconduction in a rat cranial defect model, and to quantify cortical bone porosity. Recently, microCT using high intensity and tight collimation synchrotron radiation to achieve spatial resolution of 1-2 microm has provided the capability to assess additional features such as resorption cavities. Unlike microCT, micro magnetic resonance imaging (IMRI) is nonionizing. Recently, the ability of microMRI to assess osteoporosis in animal models has been explored. Using a small, high-efficiency coil in a high-field imager, microMRI can give resolutions sufficient to discriminate individual trabeculae. We have shown that, with appropriate settings, it is possible to image trabecular bone in rats in vivo and in vitro. In our study of OVX rats, analysis of microMR images can demonstrate differences in rat trabecular bone that are not detected by DXA measurements. In a rabbit OA model, with the OA induced by meniscectomy or anterior cruciate ligament transection, MRI shows decreased cartilage thickness, subchondral osteosclerosis and osteophytes, while radiographs can only show subchondral osteosclerosis and osteophytes could not be found. Advanced imaging methods are able to measure 3D trabecular structure and connectivity in arbitrary orientations in a highly automated, objective, non-user-specific manner, allowing greater numbers of samples for unbiased comparisons between controls and the disordered or treated. They can be utilized on a large sample leading to fewer sampling errors. They are non-destructive allowing multiple tests such as biomechanical testing and chemical analysis on the same sample; and non-invasive permitting longitudinal studies and reducing the number of animals needed.     

Trabecular bone microdamage and microstructural stresses under uniaxial compression

The balance between local remodeling and accumulation of trabecular bone microdamage is believed to play an important role in the maintenance of skeletal integrity. However, the local mechanical parameters associated with microdamage initiation are not well understood. Using histological damage labeling, micro-CT imaging, and image-based finite element analysis, regions of trabecular bone microdamage were detected and registered to estimated microstructural von Mises effective stresses and strains, maximum principal stresses and strains, and strain energy density (SED). Bovine tibial trabecular bone cores underwent a stepwise uniaxial compression routine in which specimens were micro-CT imaged following each compression step. The results indicate that the mode of trabecular failure observed by micro-CT imaging agreed well with the polarity and distribution of stresses within an individual trabecula. Analysis of on-axis subsections within specimens provided significant positive relationships between microdamage and each estimated tissue stress, strain and SED parameter. In a more localized analysis, individual microdamaged and undamaged trabeculae were extracted from specimens loaded within the elastic region and to the apparent yield point. As expected, damaged trabeculae in both groups possessed significantly higher local stresses and strains than undamaged trabeculae. The results also indicated that microdamage initiation occurred prior to apparent yield at local principal stresses in the range of 88-121 MPa for compression and 35-43 MPa for tension and local principal strains of 0.46-0.63% in compression and 0.18-0.24% in tension. These data provide an important step towards understanding factors contributing to microdamage initiation and establishing local failure criteria for normal and diseased trabecular bone.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

A Comparison of Micro-CT and Dental CT in Assessing Cortical Bone Morphology and Trabecular Bone Microarchitecture

Objective

The objective of this study was to evaluate the relationship between the trabecular bone microarchitecture and cortical bone morphology by using micro-computed tomography (micro-CT) and dental cone-beam computed tomography (dental CT).

Materials and Methods

Sixteen femurs and eight fifth lumbar vertebrae were collected from eight male Sprague Dawley rats. Four trabecular bone microarchitecture parameters related to the fifth lumbar vertebral body (percent bone volume [BV/TV], trabecular thickness [TbTh], trabecular separation [TbSp], and trabecular number [TbN]) were calculated using micro-CT. In addition, the volumetric cancellous bone grayscale value (vCanGrayscale) of the fifth lumbar vertebral body was measured using dental CT. Furthermore, four cortical bone morphology parameters of the femoral diaphysis (total cross-sectional area [TtAr], cortical area [CtAr], cortical bone area fraction [CtAr/TtAr], and cortical thickness [CtTh]) were calculated using both micro-CT and dental CT. Pearson analysis was conducted to calculate the correlation coefficients (r) of the micro-CT and dental CT measurements. Paired-sample t tests were used to compare the differences between the measurements of the four cortical bone morphology parameters obtained using micro-CT and dental CT.

Results

High correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV [r = 0.84] and TbTh [r = 0.84]) measured using micro-CT were observed. The absolute value of the four cortical bone morphology parameters may be different between the dental CT and micro-CT approaches. However, high correlations (r ranged from 0.71 to 0.90) among these four cortical bone morphology parameters measured using the two approaches were obtained.

Conclusion

We observed high correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV and TbTh) measured using micro-CT, in addition to high correlations between the cortical bone morphology measured using micro-CT and dental CT. Further experiments are necessary to validate the use of dental CT on human bone.     

Spatial correlations of trabecular bone microdamage with local stresses and strains using rigid image registration

Although microdamage is known to accumulate in trabecular bone with overloading and aging, the tissue-level stresses and strains associated with local bone failure are not well known. Local correlation of microdamage with microstructural stresses and strains requires methods to accurately register histological sections with micro-computed tomography (micro-CT) based finite element models. In addition, the resolution of correlation (i.e., grid size) selected for analysis may affect the observed results. Therefore, an automated, repeatable, and accurate image registration algorithm was developed to determine the range of local stresses and strains associated with microdamage initiation. Using a two-dimensional rigid registration algorithm, bone structures from histology and micro-CT imaging were aligned. Once aligned, microdamaged regions were spatially correlated with local stresses and strains obtained from micro-CT based finite element analysis. Using this more sophisticated registration technique, we were able to analyze the effects of varying spatial grid resolution on local stresses and strains initiating microdamage. The results indicated that grid refinement to the individual pixel level (pixel-by-pixel method) more precisely defined the range of microdamage initiation compared to manually selected individual damaged and undamaged trabeculae. Using the pixel-by-pixel method, we confirmed that trabecular bone from younger cows sustained higher local strains prior to microdamage initiation compared to older bone.     

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.     

A novel downscaling approach to predict plant invasions and improve local conservation actions

To successfully protect native biodiversity from the effects of biological invasions, local conservation priorities must be established. For this purpose, fine-grained species distribution data is required but often unavailable. We present a new approach to obtain fine-grained predictions of invasion through the development of downscaled invasion maps based on coarse-grained distribution data. The framework is illustrated for the alien invader Acacia dealbata in the Northwest of Portugal. The analytical design was divided in five steps: (1) three individual coarse-grained models were calibrated and their spatial predictions were downscaled into fine-grained models using three different downscaling techniques; (2) a Downscaling Consensus Map was built by spatially combining the predictions from those three models; (3) using coarse-grained (1 km²) or fine-grained (0.04 km²) datasets, two different models were fitted and spatially projected; (4) for each spatial resolution, Conservation Value maps were produced, based on the spatial combination of the protection networks represented in the region; and (5) the spatial conflicts between the predicted distribution of the invader and Conservation Value maps were calculated and compared for the several invasion maps. The downscaled models showed high predictive performance (AUC > 0.9). The spatial projections of the different models revealed a general similarity among projections from all modelling techniques, for both the patterns of invasion and the conflicts with conservation areas. The possibility of obtaining detailed and reliable predictions based on coarse-grained distribution data could avoid costly fieldwork to collect fine-grained distribution data while effectively supporting the management of invasions at the appropriate scales.     

Finite element analysis of peri-implant bone volume affected by stresses around Morse taper implants: effects of implant positioning to the bone crest

Abstract

Objectives: The purpose of the present study was to evaluate the distribution and magnitude of stresses through the bone tissue surrounding Morse taper dental implants at different positioning relative to the bone crest. Materials and Methods: A mandibular bone model was obtained from a computed tomography scan. A three-dimensional (3D) model of Morse taper implant-abutment systems placed at the bone crest (equicrestal) and 2?mm bellow the bone crest (subcrestal) were assessed by finite element analysis (FEA). FEA was carried out on axial and oblique (45°) loading at 150 N relatively to the central axis of the implant. The von Mises stresses were analysed considering magnitude and volume of affected peri-implant bone. Results: On vertical loading, maximum von Mises stresses were recorded at 6-7?MPa for trabecular bone while values ranging from 73 up to 118?MPa were recorded for cortical bone. On oblique loading at the equiquestral or subcrestal positioning, the maximum von Mises stresses ranged from 15 to 21?MPa for trabecular bone while values at 150?MPa were recorded for the cortical bone. On vertical loading, >99.9vol.% cortical bone volume was subjected to a maximum of 2?MPa while von Mises stress values at 15?MPa were recorded for trabecular bone. On oblique loading, >99.9vol.% trabecular bone volume was subjected to maximum stress values at 5?MPa, while von Mises stress values at 35?MPa were recorded for >99.4vol.% cortical bone. Conclusions: Bone volume-based stress analysis revealed that most of the bone volume (>99% by vol) was subjected to significantly lower stress values around Morse taper implants placed at equicrestal or subcrestal positioning. Such analysis is commentary to the ordinary biomechanical assessment of dental implants concerning the stress distribution through peri-implant sites.     

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

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