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.     

Rib fractures under anterior–posterior dynamic loads: Experimental and finite-element study

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex–shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior–posterior bending loads. Then, all-hex and hex–shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex–shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force–displacement relationship predicted by both all-hex and hex–shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex–shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex–shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex–shell models. These results indicated that both all-hex and hex–shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex–shell models with constant or variable shell thickness were more computationally efficient and therefore preferred.     

Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution

The bone remodeling process takes place at the surface of trabeculae and results in a non-uniform mineral distribution. This will affect the mechanical properties of cancellous bone, because the properties of bone tissue depend on its mineral content. We investigated how large this effect is by simulating several non-uniform mineral distributions in 3D finite element models of human trabecular bone and calculating the apparent stiffness of these models. In the ‘linear model’ we assumed a linear relation between mineral content and Young's modulus of the tissue. In the ‘exponential model’ we included an empirical exponential relation in the model. When the linear model was used the mineral distribution slightly changed the apparent stiffness, the difference varied between an 8% decrease and a 4% increase compared to the uniform model with the same BMD. The exponential model resulted in up to 20% increased apparent stiffness in the main load-bearing direction. A thin less mineralized surface layer (28 μm) and highly mineralized interstitial bone (mimicking mineralization resulting from anti-resorptive treatment) resulted in the highest stiffness. This could explain large reductions in fracture risk resulting from small increases in BMD. The non-uniform mineral distribution could also explain why bone tissue stiffness determined using nano-indentation is usually higher than finite element (FE)-determined stiffness. We conclude that the non-uniform mineral distribution in trabeculae does affect the mechanical properties of cancellous bone and that the tissue stiffness determined using FE-modeling could be improved by including detailed information about mineral distribution in trabeculae in the models.     

Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.     

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.     

The presence of the potentially toxic genera Ostreopsis and Coolia (Dinophyceae) in the North Aegean Sea, Greece

The examination of macrophyte, water and sediment samples, collected at depths less than 1.5 m from 50 different sites along the North Aegean coasts, has revealed, for the first time in Greek coastal waters, the presence of two Ostreopsis species (O. ovata and O. cf. siamensis) and Coolia monotis in the majority of the sampling sites (94% and 100%, respectively). Other epiphytic dinoflagellates of the genera Prorocentrum and Amphidinium and diatoms were accompanying species in this epiphytic community. Morphometric features, plate formula and thecal ornamentation were used for species identification. O. ovata cells were smaller in dorsoventral (DV) diameter and width (W) (26.18–61.88 μm and 13.09–47.60 μm, respectively) in comparison with O. cf. siamensis (35.70–65.45 μm and 23.80–49.98 μm, respectively). In contrast, the anterioposterior (AP) diameter of O. cf. siamensis was smaller (14.28–26.18 μm) resulting in DV/AP ≈ 3, whereas the above ratio for O. ovata was less than 2 (AP ranging between 14.28–35.70 μm). Moreover, the theca of O. ovata cells was ornamented with scattered pores, which fluctuated in a wider range (0.07–0.32 μm) than those of O. cf. siamensis (0.23–0.29 μm). Coolia monotis cells were almost round with average DV diameter 26.88 μm, AP 25.66 μm and width 26.76 μm. Small and large cells were recorded in both field and culture populations of Ostreopsis spp. and C. monotis, while hyaline cysts were observed for O. ovata. The presence of O. ovata and O. cf. siamensis exhibited a clear seasonal pattern dominating (maximum abundance up to 4.05 × 10⁵ cells gr⁻¹ fwm) the period from midsummer to late autumn in years 2003 and 2004, while C. monotis was found also in winter and spring months.     

Effects of geometry on transmission and sensing potential of tapered fiber sensors

Geometry of tapered fiber sensors critically affects the response of an evanescent field sensor to cell suspensions. Single-mode fibers (nominally at 1300 nm) were tapered to symmetric or asymmetric tapers with diameters in the range of 3–20 μm, and overall lengths of 1–7 mm. Their transmission characteristics in air, water and in the presence of Escherichia coli (JM101 strain) at concentrations of 100, 1000, 7000 and 7 million cells/mL were measured in the 400–800 nm range and gave rich spectral data that lead to the following conclusions. (1) No change in transmission was observed due to E. coli with tapers that showed no relative change in transmission in water compared to air. (2) Tapers that exhibited a significant difference in transmission in water compared to air gave weak response to the presence of the E. coli. Of these, tapers with low waist diameters (6 μm) showed sensitivity to E. coli at 7000 cells/mL and higher concentration. (3) Tapers that showed modest difference in water transmission compared to air, and those that had small waist diameters gave excellent response to E. coli at 100–7000 cells/mL. In addition, mathematical modeling showed that: (1) at low wavelength (470 nm) and small waist diameter (6 μm), transmission with water in the waist region is higher than in air. (2) Small changes in waist diameter (0.05 μm) can cause larger changes in transmission at 470 nm than at 550 nm at waist diameter of 6 μm. (3) For the same overall geometry, a 5.5 μm diameter taper showed larger refractive index sensitivity compared to a 6.25 μm taper at 470 nm.     

Finite element model development of a child pelvis with optimization-based material identification

A finite element (FE) model of a 10-years-old child pelvis was developed and validated against experimental data from lateral impacts of pediatric pelves. The pelvic bone geometry was reconstructed from a set of computed tomography images, and a hexahedral mesh was generated using a new octree-based hexahedral meshing technique. Lateral impacts to the greater trochanter and iliac wing of the seated pelvis were simulated. Sensitivity analysis was conducted to identify material parameters that substantially affected the model response. An optimization-based material identification method was developed to obtain the most favorable material property set by minimizing differences in biomechanical responses between experimental and simulation results. This study represents a pilot effort in the development and validation of age-dependent musculoskeletal FE models for children, which may ultimately serve to evaluate injury mechanisms and means of protection for the pediatric population.     

Introduction and evaluation of a gray-value voxel conversion technique

In micro finite element analyses (microFEA) of cancellous bone, the 3D-imaging data that the FEA-models are based on, contain a range of gray-values. In the construction of the eventual FEA-model, these gray-values are commonly thresholded. Although thresholding is successful at small voxel sizes, at larger voxel sizes there is substantial loss of trabecular connectivity. We propose a new method: the gray-value method, where the microFEA-models use the information within the 3D-imaging data directly, without prior thresholding. Our question was twofold. First, how does the gray-value method compare to both plain and mass-compensated thresholding? Second, what is the effect of element size on the results obtained with the gray-value method? We used nine microCT-scans of human vertebral cancellous bone. These were degraded to represent different resolutions, and converted into microFEA-models using plain thresholding, mass-compensated thresholding, and the gray-value method. The apparent elastic moduli of the specimens were determined using microFEA. The different methods were compared on the basis of the apparent elastic moduli, compared to those calculated for a 28 microm reference model. The results showed that the gray-value method greatly improves the results relative to other methods. The gray-value method gives accurate predictions of the apparent elastic moduli, for voxel sizes up to one trabecular thickness (Tb.Th.). For voxel sizes greater than one Tb.Th. the accuracy, although still better than for both thresholding methods, becomes increasingly worse.     

Distributional Variations in Trabecular Architecture of the Mandibular Bone: An In Vivo Micro-CT Analysis in Rats

Purpose

To evaluate the effect of trabecular thickness and trabecular separation on modulating the trabecular architecture of the mandibular bone in ovariectomized rats.

Materials and Methods

Fourteen 12-week-old adult female Wistar rats were divided into an ovariectomy group (OVX) and a sham-ovariectomy group (sham). Five months after the surgery, the mandibles from 14 rats (seven OVX and seven sham) were analyzed by micro-CT. Images of inter-radicular alveolar bone of the mandibular first molars underwent three-dimensional reconstruction and were analyzed.

Results

Compared to the sham group, trabecular thickness in OVX alveolar bone decreased by 27% (P = 0.012), but trabecular separation in OVX alveolar bone increased by 59% (P = 0.005). A thickness and separation map showed that trabeculae of less than 100μm increased by 46%, whereas trabeculae of more than 200μm decreased by more than 40% in the OVX group compared to those in the sham group. Furthermore, the OVX separation of those trabecular of more than 200μm was 65% higher compared to the sham group. Bone mineral density (P = 0.028) and bone volume fraction (p = 0.001) were also significantly decreased in the OVX group compared to the sham group.

Conclusions

Ovariectomy-induced bone loss in mandibular bone may be related to the distributional variations in trabecular thickness and separation which profoundly impact the modulation of the trabecular architecture.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

A finite element beam-model for efficient simulation of large-scale porous structures

This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.     

Mesh-morphing algorithms for specimen-specific finite element modeling

Despite recent advances in software for meshing specimen-specific geometries, considerable effort is still often required to produce and analyze specimen-specific models suitable for biomechanical analysis through finite element modeling. We hypothesize that it is possible to obtain accurate models by adapting a pre-existing geometry to represent a target specimen using morphing techniques. Here we present two algorithms for morphing, automated wrapping (AW) and manual landmarks (ML), and demonstrate their use to prepare specimen-specific models of caudal rat vertebrae. We evaluate the algorithms by measuring the distance between target and morphed geometries and by comparing response to axial loading simulated with finite element (FE) methods.

First a traditional reconstruction process based on μCT was used to obtain two natural specimen-specific FE models. Next, the two morphing algorithms were used to compute mappings from the surface of one model, the source, to the other, the target, and to use this mapping to morph the source mesh to produce a target mesh. The μCT images were then used to assign element-specific material properties. In AW the mappings were obtained by wrapping the source and target surfaces with an auxiliary triangulated surface. In ML, landmarks were manually placed on corresponding locations on the surfaces of both source and target.

Both morphing algorithms were successful in reproducing the shape of the target vertebra with a median distance between natural and morphed models of 18.8 and 32.2 μm, respectively, for AW and ML. Whereas AW–morphing produced a surface more closely resembling that of the target, ML guaranteed correspondence of the landmark locations between source and target. Morphing preserved the quality of the mesh producing models suitable for FE simulation. Moreover, there were only minor differences between natural and morphed models in predictions of deformation, strain and stress. We therefore conclude that it is possible to use mesh-morphing techniques to produce accurate specimen-specific FE models of caudal rat vertebrae. Mesh morphing techniques provide advantages over conventional specimen-specific finite element modeling by reducing the effort required to generate multiple target specimen models, facilitating intermodel comparisons through correspondence of nodes and maintenance of connectivity, and lends itself to parametric evaluation of “artificial” geometries with a focus on optimizing reconstruction.     

Staining and Histomorphometry of Microcracks in the Human Femoral Head

We developed staining techniques that permit identification and histomorphometric analysis of microcracks in the human femoral head 1) from thick, ground bone sections (100 μm) by prestaining with the Villanueva mineralized bone stain (MIBS), and 2) from plastic embedded, undecalcified thin bone sections (5-15 μm) by staining in gallocyanin chrome alum-Villanueva blood stain methods. Both methods represent a significant improvement in the stainability of the microcracks, cellular and tissue elements, and the simultaneous assessment of osteoid seams and tetracycline markers by histomorphometry. Shrinkage and other artifacts were minimized, which helped to clarify some of the uncertainties arising from artifacts resulting from some bone staining methods. Histomorphometric analyses of microcracks were conducted on thick, ground sections of subchondral and trabecular bone. Microcracks were more prevalent in the subchondral bone and osteochondral junction than in the more distant trabeculae. We have consistently localized microcrack areas in bone tissues prepared in these ways.     

A Three-Dimensional Histological Method for Direct Determination of the Number of Trabecular Termini in Cancellous Bone

Osteoporotic fractures occur frequently in aging populations. Established methods for analyzing microarchitecture indicate that cancellous bone loss in the elderly is associated with progressive reduction in the connectivity of the trabecular network. This disconnection may explain the increased skeletal fragility that is sometimes out of proportion to the amount of bone lost. Connectivity, however, is difficult to measure and usually requires indirect methods. We describe development of a simple, inexpensive and direct procedure for counting sites of trabecular disconnection. The method is based upon preparation of 300-500 fjim thick slices of methylmethacrylate embedded material rather than the more usual thin 8 μm. histological sections. The marrow tissue is retained within the thick slice; this is essential for conservation of any detached bone fragments. In such preparations differential superficial staining of the upper and lower surfaces with alizarin red and light green, respectively, allows the two-dimensional image to be viewed at the same time as its three-dimensional counterpart. In this way, “real” (i. e., unstained) trabecular termini can be distinguished from “apparent” (i. e., stained red or green) termini that are artifacts of the plane of section. Partly polarized light enhances the microscope image. The method does not destroy the material for subsequent bone histomorphom-etry and, therefore, may be a useful adjunct to iliac bone biopsy analysis in studies of metabolic bone disease.     

Synthesis and in vitro anti-hepatitis B and C virus activities of ring-expanded ('fat') nucleobase analogues containing the imidazo[4,5-e][1,3]diazepine-4,8-dione ring system

As part of our structure–activity relationship studies, we report here the synthesis and in vitro anti-HBV and anti-HCV activities of a number of ring-expanded (‘fat’) nucleobases containing the imidazo[4,5-e][1,3]diazepine-4,8-dione ring system. One of the compounds, ZP-88, exhibited a good activity/toxicity profile against HBV by inhibition of the synthesis of extracellular virion release (EC₅₀ = 1.7 μM, CC₅₀ = 286 μM, SI = 168) and intracellular HBV replication intermediates (EC₅₀ = 8.4 μM, CC₅₀ = 286 μM, SI = 34) in cultured human hepatoblastoma 2.2.15 cells. By contrast, most of the compounds tested against HCV had only marginal activity/toxicity profile, although that was still better than that of the reference compound ribavirin.     

The effect of resorption cavities on bone stiffness is site dependent

Resorption cavities formed during the bone remodelling cycle change the structure and thus the mechanical properties of trabecular bone. We tested the hypotheses that bone stiffness loss due to resorption cavities depends on anatomical location, and that for identical eroded bone volumes, cavities would cause more stiffness loss than homogeneous erosion. For this purpose, we used beam–shell finite element models. This new approach was validated against voxel-based FE models. We found an excellent agreement for the elastic stiffness behaviour of individual trabeculae in axial compression (R² = 1.00) and in bending (R²>0.98), as well as for entire trabecular bone samples to which resorption cavities were digitally added (R² = 0.96, RMSE = 5.2%). After validation, this new method was used to model discrete cavities, with dimensions taken from a statistical distribution, on a dataset of 120 trabecular bone samples from three anatomical sites (4th lumbar vertebra, femoral head, iliac crest). Resorption cavities led to significant reductions in bone stiffness. The largest stiffness loss was found for samples from the 4th lumbar vertebra, the lowest for femoral head samples. For all anatomical sites, resorption cavities caused significantly more stiffness loss than homogeneous erosion did. This novel technique can be used further to evaluate the impact of resorption cavities, which are known to change in several metabolic bone diseases and due to treatment, on bone competence.     

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.     

Apigenin inhibits osteoblastogenesis and osteoclastogenesis and prevents bone loss in ovariectomized mice

Polyphenol have been reported to have physiological effects with respect to alleviating diseases such as osteoporosis and osteopetrosis. We recently reported that the olive polyphenol hydroxytyrosol accelerates bone formation both in vivo and in vitro. The present study was designed to evaluate the in vivo and in vitro effects of apigenin (4′,5,7-trihydroxyflavone), one of the major polyphenols in olives and parsley, on bone formation by using cultured osteoblasts and osteoclasts and ovariectomized (OVX) mice, respectively. Apigenin markedly inhibited cell proliferation and indices of osteoblast differentiation, such as collagen production, alkaline phosphatase activity, and calcium deposition in osteoblastic MC3T3-E1 cells at concentrations of 1–10 μM. At 10 μM, apigenin completely inhibited the formation of multinucleated osteoclasts from mouse splenic cells. Moreover, injection of apigenin at 10 mg kg⁻¹ body weight significantly suppressed trabecular bone loss in the femurs of OVX mice. Our findings indicate that apigenin may have critical effects on bone maintenance in vivo.