Principal trabecular structural orientation predicted by quantitative ultrasound is strongly correlated with \upmu FEA determined anisotropic apparent stiffness

The microarchitecture and alignment of trabecular bone adapts to the particular mechanical milieu applied to it. Due to this anisotropic mechanical property, measurement orientation has to be taken into consideration when assessing trabecular bone quality and fracture risk prediction. Quantitative ultrasound (QUS) has demonstrated the ability in predicting the principal structural orientation (PSO) of trabecular bone. Although the QUS prediction for PSO is very close to that of \(\upmu \) CT, certain angle differences still exist. It remains unknown whether this angle difference can induce significant differences in mechanical properties or not. The objective of this study was to evaluate the mechanical properties in different PSOs predicted using different methods, QUS and \(\upmu \) CT, thus to investigate the ability of QUS as a means to predict the PSO of trabecular bone noninvasively. By validating the ability of QUS to predict the PSO of trabecular bone, it is beneficial for future QUS applications because QUS measurements in the PSO can provide information more correlated with the mechanical properties than with other orientations. In this study, seven trabecular bone balls from distal bovine femurs were used to generate finite element models based on the 3-dimensional \(\upmu \) CT images. Uniaxial compressive loading was performed on the bone ball models in the finite element analysis (FEA) in six different orientations (three anatomical orientations, two PSOs predicted by QUS and the longest vector of mean intercept length (MIL) tensor calculated by \(\upmu \) CT). The stiffness was calculated based on the reaction force of the bone balls under loading, and the von Mises stress results showed that both the mechanical properties in the PSOs predicted by QUS are significantly higher than the anatomical orientations and comparatively close to the longest vector of MIL tensor. The stiffness in the PSOs predicted by QUS is also highly correlated with the stiffness in the MIL tensor orientation (ATTmax vs. MIL, \(R^{2}\)  = 0.98, \(p<001\) ; UVmax vs. MIL, \(R^{2}\)  = 0.92, \(p<001\) ). These results were validated by in vitro mechanical testing on the bone ball samples. This study demonstrates that the PSO of trabecular bone predicted by QUS has an equally strong apparent stiffness with the orientation predicted by \(\upmu \) CT.     

Validation of composite finite elements efficiently simulating elasticity of trabecular bone

Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r_𝒸 ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.     

Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=−0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.     

Angular orientation of trabecular bone in the femoral head and its relationship to hip joint loads in leaping primates

The elastic properties and mechanical behavior of trabecular bone are largely determined by its three-dimensional (3D) fabric structure. Recent work demonstrating a correlation between the primary mechanical and material axes in trabecular bone specimens suggests that fabric orientation may be used to infer directional components of the material strength and, by extension, the hypothetical loading regime. Here we quantify the principal orientation of trabecular bone in the femoral head and relate these principal fabric directions to loading patterns during various locomotor behaviors. The proximal femora of a diverse sample of prosimians were scanned using a high-resolution X-ray computed tomography scanner with resolution of better than 50 mum. Spherical volumes of interest were defined within the femoral heads and the 3D fabric anisotropy was calculated using the mean intercept length and star volume distribution methods. In addition to differences in bone volume and anisotropy, significant differences were found in the spatial orientation of the principal trabecular axes depending on locomotor behavior. The principal orientations for leapers (Galago, Tarsius, Avahi) are relatively tightly clustered (alpha(95) confidence limit: 8.2; angular variance s: 18.2 degrees ) and oriented in a superoanterior direction, while those of nonleapers are more variable across a range of directions (alpha(95): 16.8; s: 42.0 degrees ). The mean principal directions are significantly different for leaping vs. nonleaping taxa. These results further suggest a relationship between bone microstructure in the hip joint and locomotor behavior and indicate a similarity of loading across leapers despite differences in kinematics and phylogeny.     

Prediction of trabecular bone principal structural orientation using quantitative ultrasound scanning

Bone has the ability to adapt its structure in response to the mechanical environment as defined as Wolff's Law. The alignment of trabecular structure is intended to adapt to the particular mechanical milieu applied to it. Due to the absence of normal mechanical loading, it will be extremely important to assess the anisotropic deterioration of bone during the extreme conditions, i.e., long term space mission and disease orientated disuse, to predict risk of fractures. The propagation of ultrasound wave in trabecular bone is substantially influenced by the anisotropy of the trabecular structure. Previous studies have shown that both ultrasound velocity and amplitude is dependent on the incident angle of the ultrasound signal into the bone sample. In this work, seven bovine trabecular bone balls were used for rotational ultrasound measurement around three anatomical axes to elucidate the ability of ultrasound to identify trabecular orientation. Both ultrasound attenuation (ATT) and fast wave velocity (UV) were used to calculate the principal orientation of the trabecular bone. By comparing to the mean intercept length (MIL) tensor obtained from μCT, the angle difference of the prediction by UV was 4.45°, while it resulted in 11.67° angle difference between direction predicted by μCT and the prediction by ATT. This result demonstrates the ability of ultrasound as a non-invasive measurement tool for the principal structural orientation of the trabecular bone.     

Determining the Cellular Structure of Two Cereal Food Foams by X-ray Micro-Tomography

The cellular structure of two products, an extruded breakfast cereal and a short dough biscuit, was characterized by two different X-ray micro computed tomographic systems. Acquisitions were made by a compact desktop system Skyscan 1174 (Bruker μCT, Belgium) and at the European Synchrotron Radiation Facility (ESRF, beamline ID19, France) at different resolutions (voxel size of 6.5 μm, 7.5 μm, 16.2 μm and 25.8 μm). 3D images were processed for the density, the connectivity index and the granulometry of cells and cell walls. These experiments underlined the importance of the resolution for determination of quantitative measurements such as densities and thicknesses. The median width calculated for the cell walls distribution in the biscuit dropped from 141 to 50 μm when the voxel size changed from 25.8 to 7.5 μm. Images well showed that even though the food products had close values of porosity 0.6 and 0.7 for biscuit and extruded breakfast cereal respectively, their cellular structures were very different. The biscuit had small cells (median value of the distribution varied from 125 to 152 μm, according to resolution) and larger cell walls (50–141 μm) than the extrudate (32–109 μm) which, on the contrary, exhibited very large cells (307–400 μm). Beyond methodological issues, these differences could be clearly attributed to the differences of compositions and processes.     

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.     

Trabecular bone adaptation with an orthotropic material model.

Most bone adaptation algorithms, that attempt to explain the connection between bone morphology and loads, assume that bone is effectively isotropic. An isotropic material model can explain the bone density distribution, but not the structure and pattern of trabecular bone, which clearly has a mechanical significance. In this paper, an orthotropic material model is utilized to predict the proximal femur trabecular structure. Two hypotheses are combined to determine the local orientation and material properties of each element in the model. First, it is suggested that trabecular directions, which correspond to the orthotropic material axes, are determined locally by the maximal principal stress directions due to the multiple load cases (MLC) the femur is subject to. The second hypothesis is that material properties in each material direction can be determined using directional stimuli, thus extending existing adaptation algorithms to include directionality. An algorithm is utilized, where each iteration comprises of two stages. First, material axes are rotated to the direction of the largest principal stress that occurs from a multiple load scheme applied to the proximal femur. Next, material properties are modified in each material direction, according to a directional stimulus. Results show that local material directions correspond with known trabecular patterns, reproducing all main groups of trabeculae very well. The local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.     

Micro-computed tomography image-based evaluation of 3D anisotropy degree of polymer scaffolds

Anisotropy is one of the most meaningful determinants of biomechanical behaviour. This study employs micro-computed tomography (μCT) and image techniques for analysing the anisotropy of regenerative medicine polymer scaffolds. For this purpose, three three-dimensional anisotropy evaluation image methods were used: ellipsoid of inertia (EI), mean intercept length (MIL) and tensor scale (t-scale). These were applied to three patterns (a sphere, a cube and a right prism) and to two polymer scaffold topologies (cylindrical orthogonal pore mesh and spherical pores). For the patterns, the three methods provided good results. Regarding the scaffolds, EI mistook both topologies (0.0158, [ ? 0.5683; 0.6001]; mean difference and 95% confidence interval), and MIL showed no significant differences (0.3509, [0.0656; 0.6362]). T-scale is the preferable method because it gave the best capability (0.3441, [0.1779; 0.5102]) to differentiate both topologies. This methodology results in the development of non-destructive tools to engineer biomimetic scaffolds, incorporating anisotropy as a fundamental property to be mimicked from the original tissue and permitting its assessment by means of μCT image analysis.     

Relationships between loading history and femoral cancellous bone architecture

A theory relating bone maintenance to mechanical loading history has been applied to successfully predict the distribution of bone density and trabecular orientation in the adult proximal femur. The loading history was simulated by determining the stress fields in a two-dimensional finite element model exposed to various discrete loading cases and making assumptions about the relative number of loading cycles associated with each load case. The total stimulus to bone maintenance was then calculated by a linear superposition of the stimulus of each loading case. Based on the calculated total stimulus, the apparent density and material properties of each element were changed and the stress solutions were again determined. Using this iterative technique, the bone apparent density and orientation characteristics were predicted. The results indicate that the trabecular morphology of the femur can only be explained by considering the joint loadings from multiple directions. Contrary to the 'trajectorial theory' promoted by Wolff (The Law of Bone Remodelling, 1892), trabecular orientations predicted from our multiple-load analyses are not necessarily perpendicular and do not correspond to the principal stress directions of any one loading condition. Our predicted orientations correspond better to the drawing of bone trabecular morphology by von Meyer (Archs Anat. Physiol. wiss. Med. 34, 615-628, 1867) than to the classic drawing by Wolff and suggest that further study of the trajectorial theory is warranted.     

Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors

The apparent stiffness tensor is an important mechanical parameter for characterizing trabecular bone. Previous studies have modeled this parameter as a function of mechanical properties of the tissue, bone density, and a second-order fabric tensor, which encodes both anisotropy and orientation of trabecular bone. Although these models yield strong correlations between observed and predicted stiffness tensors, there is still space for reducing accuracy errors. In this paper, we propose a model that uses fourth-order instead of second-order fabric tensors. First, the totally symmetric part of the stiffness tensor is assumed proportional to the fourth-order fabric tensor in the logarithmic scale. Second, the asymmetric part of the stiffness tensor is derived from relationships among components of the harmonic tensor decomposition of the stiffness tensor. The mean intercept length (MIL), generalized MIL (GMIL), and fourth-order global structure tensor were computed from images acquired through microcomputed tomography of 264 specimens of the femur. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (\(\upmu \)FE), which was considered as the gold standard, yielding strong correlations (\(R^2\) above 0.962). The GMIL tensor yielded the best results among the tested fabric tensors. The Frobenius error, geodesic error, and the error of the norm were reduced by applying the proposed model by 3.75, 0.07, and 3.16 %, respectively, compared to the model by Zysset and Curnier (Mech Mater 21(4):243–250, 1995) with the second-order MIL tensor. From the results, fourth-order fabric tensors are a good alternative to the more expensive \(\upmu \)FE stiffness predictions.     

Vertebral trabecular main direction can be determined from clinical CT datasets using the gradient structure tensor and not the inertia tensor—A case study

Osteoporosis is a wide spread disease with one-third of all women beyond their menopause and a fifth of men above the age of 50 years suffering from it. Patient specific finite element models would be a great improvement for the diagnosis of vertebral fracture risk. Different material models have been proposed, which incorporate information about the anisotropy of trabecular bone in addition to bone mineral density (BMD) using a second rank structure tensor.Two alternative structure measurement methods, gradient structure tensor (GST) and inertia tensor (IT), were investigated. Structure was determined from in situ scans. This was compared to structure computed with the mean intercept length (MIL) tensor from $\mathrm{\mu }\mathrm{CT}$ scans at the same locations.GST delivered information comparable to MIL regarding the structural main direction even at normal dose standard clinical settings (median of the scalar products of up to $\approx 0.98$). IT was not comparable to MIL (median $\approx 0.4$). Neither of the alternatives could determine eigenvalues comparable to these determined from MIL ($p>0.5$).In conclusion, this study could show that the measurement of the structural main direction is possible for in situ scans in a clinical setting. It was shown that the method of choice to determine trabecular main direction in situ is GST. Knowing the main direction a transverse isotropic fabric tensor can be constructed.     

A novel approach to estimate trabecular bone anisotropy using a database approach

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models.     

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.     

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.     

Fluid–structure interactions in micro-interlocked regions of the cement–bone interface

Experimental tests and computational modelling were used to explore the fluid dynamics at the trabeculae–cement interlock regions found in the tibial component of total knee replacements. A cement–bone construct of the proximal tibia was created to simulate the immediate post-operative condition. Gap distributions along nine trabeculae–cement regions ranged from 0 to 50.4 μm (mean = 12 μm). Micro-motions ranged from 0.56 to 4.7 μm with a 1 MPa compressive load to the cement. Fluid–structure analysis between the trabeculae and the cement used idealised models with parametric evaluation of loading direction, gap closing fraction (GCF), gap thickness, loading frequency and fluid viscosity. The highest fluid shear stresses (926 Pa) along the trabecular surface were found for conditions with very thin and large GCFs, much larger than reported physiological levels (～1–5 Pa). A second fluid–structure model was created with a provision for bone resorption using a constitutive model with resorption velocity proportional to fluid shear rate. A lower cut-off was used, below which bone resorption would not occur (50 s^? 1). Results showed that there was initially high shear rates (>1000 s^? 1) that diminished after initial trabecular resorption. Resorption continued in high shear rate regions, resulting in a final shape with bone left deep in the cement layer, and is consistent with morphology found in post-mortem retrievals. Small gaps between the trabecular surface and the cement in the immediate post-operative state produce fluid flow conditions that appear to be supra-physiologic; these may cause fluid-induced lysis of trabeculae in the micro-interlock regions.     

Influence of anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study

Although the biomechanical behavior of the acetabular cup (AC) implant is determinant for the surgical success, it remains difficult to be assessed due to the multiscale and anisotropic nature of bone tissue. The aim of the present study was to investigate the influence of the anisotropic properties of peri-implant trabecular bone tissue on the biomechanical behavior of the AC implant at the macroscopic scale. Thirteen bovine trabecular bone samples were imaged using micro-computed tomography (μCT) with a resolution of 18 μm. The anisotropic biomechanical properties of each sample were determined at the scale of the centimeter based on a dedicated method using asymptotic homogenization. The material properties obtained with this multiscale approach were used as input data in a 3D finite element model to simulate the macroscopic mechanical behavior of the AC implant under different loading conditions. The largest stress and strain magnitudes were found around the equatorial rim and in the polar area of the AC implant. All macroscopic stiffness quantities were significantly correlated (R² > 0.85, p < 6.5 e-6) with BV/TV (bone volume/total volume). Moreover, the maximum value of the von Mises stress field was significantly correlated with BV/TV (R² > 0.61, p < 1.6 e-3) and was always found at the bone-implant interface. However, the mean value of the microscopic stress (at the scale of the trabeculae) decrease as a function of BV/TV for vertical and torsional loading and do not depend on BV/TV for horizontal loading. These results highlight the importance of the anisotropic properties of bone tissue.     

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.     

Registration of 2D histological sections with 3D micro-CT datasets from small animal vertebrae and tibiae

The aim of this study was the registration of digitized thin 2D sections of mouse vertebrae and tibiae used for histomorphometry of trabecular bone structure into 3D micro computed tomography (μCT) datasets of the samples from which the sections were prepared. Intensity-based and segmentation-based registrations (SegRegs) of 2D sections and 3D μCT datasets were applied. As the 2D sections were deformed during their preparation, affine registration for the vertebrae was used instead of rigid registration. Tibiae sections were additionally cut on the distal end, which subsequently undergone more deformation so that elastic registration was necessary. The Jaccard distance was used as registration quality measure. The quality of intensity-based registrations and SegRegs was practically equal, although precision errors of the elastic registration of segmentation masks in tibiae were lower, while those in vertebrae were lower for the intensity-based registration. Results of SegReg significantly depended on the segmentation of the μCT datasets. Accuracy errors were reduced from approximately 64% to 42% when applying affine instead of rigid transformations for the vertebrae and from about 43% to 24% when using B-spline instead of rigid transformations for the tibiae. Accuracy errors can also be caused by the difference in spatial resolution between the thin sections (pixel size: 7.25 μm) and the μCT data (voxel size: 15 μm). In the vertebrae, average deformations amounted to a 6.7% shortening along the direction of sectioning and a 4% extension along the perpendicular direction corresponding to 0.13–0.17 mm. Maximum offsets in the mouse tibiae were 0.16 mm on average.     

Micro-finite element simulation of trabecular-bone post-yield behaviour – effects of material model,element size and type

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 μm had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.