Homogenized finite element analysis of distal tibia sections: Achievements and limitations.

High-resolution peripheral quantitative computed tomography (HR-pQCT) based micro-finite element (µFE) analysis allows accurate prediction of stiffness and ultimate load of standardised (∼1 cm) distal radius and tibia sections. An alternative homogenized finite element method (hFE) was recently validated to compute the ultimate load of larger (∼2 cm) distal radius sections that include Colles' fracture sites. Since the mechanical integrity of the weight-bearing distal tibia is gaining clinical interest, it has been shown that the same properties can be used to predict the strength of both distal segments of the radius and the tibia. Despite the capacity of hFE to predict structural properties of distal segments of the radius and the tibia, the limitations of such homogenization scheme remain unclear. Therefore, the objective of this study is to build a complete mechanical data set of the compressive behavior of distal segments of the tibia and to compare quantitatively the structural properties with the hFE predictions. As a further aim, it is intended to verify whether hFE is also able to capture the post-yield strain localisation or fracture zones in such a bone section, despite the absence of strain softening in the constitutive model. Twenty-five fresh-frozen distal parts of tibias of human donors were used in this study. Sections were cut corresponding to an in-house triple-stack protocol HR-pQCT scan, lapped, and scanned using micro computed tomography (µCT). The sections were tested in compression until failure, unloaded and scanned again in µCT. Volumetric bone mineral density (vBMD) and bone mineral content (BMC) were correlated to compression test results. hFE analysis was performed in order to compare computational predictions (stiffness, yield load and plastic deformation field pattern) with the compressive experiment. Namely, strain localization was assessed based on digital volume correlation (DVC) results and qualitatively compared to hFE predictions by comparing mid-slices patterns. Bone mineral content (BMC) showed a good correlation with stiffness (R2 = 0.92) and yield (R2 = 0.88). Structural parameters also showed good agreement between the experiment and hFE for both stiffness (R2 = 0.96, slope = 1.05 with 95 % CI [0.97, 1.14]) and yield (R2 = 0.95, slope = 1.04 [0.94, 1.13]). The qualitative comparison between hFE and DVC strain localization patterns allowed the classification of the samples into 3 categories: bad (15 sections), semi (8), and good agreement (2). The good correlations between BMC or hFE and experiment for structural parameters were similar to those obtained previously for the distal part of the radius. The failure zones determined by hFE corresponded to registration only in 8 % of the cases. We attribute these discrepancies to local elastic/plastic buckling effects that are not captured by the continuum-based FE approach exempt from strain softening. A way to improve strain localization hFE prediction would be to use longer distal segments with intact cortical shells, as done for the radius. To conclude, the used hFE scheme captures the elastic and yield response of the tibia sections reliably but not the subsequent failure process.

Does tissue fixation change the mechanical properties of dry ovine bone extracellular matrix?

Tissue fixation is a prevalent method for bone conservation. Bone biopsies are typically fixed in formalin, dehydrated in ethanol, and infiltrated with polymethyl methacrylate (PMMA) Since some experiments can only be performed on fixed bone samples, it is essential to understand how fixation affects the measured material properties. The aim of this study was to quantify the influence of tissue fixation on the mechanical properties of cortical ovine bone at the extracellular matrix (ECM) level with state-of-the-art micromechanical techniques. A small section from the middle of the diaphysis of two ovine tibias (3.5 and 5.5 years old) was cut in the middle and polished on each side, resulting in a pair of mirrored surfaces. For each pair, one specimen underwent a fixation protocol involving immersion in formalin, dehydration with ethanol, and infiltration with PMMA. The other specimen (mirrored) was air-dried. Six osteons were selected in both pairs, which could be identified in both specimens. The influence of fixation on the mechanical properties was first analyzed using micropillar compression tests and nanoindentation in dry condition. Additionally, changes in the degree of mineralization were evaluated with Raman spectroscopy in both fixed and native bone ECM. Finally, micro tensile experiments were conducted in the 3.5-year fixed ovine bone ECM and compared to reported properties of unfixed dry ovine bone ECM. Interestingly, we found that tissue fixation does not alter the mechanical properties of ovine cortical bone ECM compared to experiments in dry state. However, animal age increases the degree of mineralization (p = 0.0159) and compressive yield stress (p = 0.041). Tissue fixation appears therefore as a valid conservation technique for investigating the mechanical properties of dehydrated bone ECM.

Tensile Mechanical Properties of Dry Cortical Bone Extracellular Matrix: A Comparison Among Two Osteogenesis Imperfecta and One Healthy Control Iliac Crest Biopsies.

Osteogenesis imperfecta (OI) is a genetic, collagen-related bone disease that increases the incidence of bone fractures. Still, the origin of this brittle mechanical behavior remains unclear. The extracellular matrix (ECM) of OI bone exhibits a higher degree of bone mineralization (DBM), whereas compressive mechanical properties at the ECM level do not appear to be inferior to healthy bone. However, it is unknown if collagen defects alter ECM tensile properties. This study aims to quantify the tensile properties of healthy and OI bone ECM. In three transiliac biopsies (healthy n = 1, OI type I n = 1, OI type III n = 1), 23 microtensile specimens (gauge dimensions 10 × 5 × 2 µm3) were manufactured and loaded quasi-statically under tension in vacuum condition. The resulting loading modulus and ultimate strength were extracted. Interestingly, tensile properties in OI bone ECM were not inferior compared to controls. All specimens revealed a brittle failure behavior. Fracture surfaces were graded according to their mineralized collagen fibers (MCF) orientation into axial, mixed, and transversal fracture surface types (FST). Furthermore, tissue mineral density (TMD) of the biopsy cortices was extracted from micro-computed tomogra[hy (µCT) images. Both FST and TMD are significant factors to predict loading modulus and ultimate strength with an adjusted R 2 of 0.556 (p = 2.65e-05) and 0.46 (p = 2.2e-04), respectively. The influence of MCF orientation and DBM on the mechanical properties of the neighboring ECM was further verified with quantitative polarized Raman spectroscopy (qPRS) and site-matched nanoindentation. MCF orientation and DBM were extracted from the qPRS spectrum, and a second mechanical model was developed to predict the indentation modulus with MCF orientation and DBM (R 2 = 67.4%, p = 7.73e-07). The tensile mechanical properties of the cortical bone ECM of two OI iliac crest biopsies are not lower than the one from a healthy and are primarily dependent on MCF orientation and DBM. © 2023 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Composition and micromechanical properties of the femoral neck compact bone in relation to patient age, sex and hip fracture occurrence.

Current clinical methods of bone health assessment depend to a great extent on bone mineral density (BMD) measurements. However, these methods only act as a proxy for bone strength and are often only carried out after the fracture occurs. Besides BMD, composition and tissue-level mechanical properties are expected to affect the whole bone's strength and toughness. While the elastic properties of the bone extracellular matrix (ECM) have been extensively investigated over the past two decades, there is still limited knowledge of the yield properties and their relationship to composition and architecture. In the present study, morphological, compositional and micropillar compression bone data was collected from patients who underwent hip arthroplasty. Femoral neck samples from 42 patients were collected together with anonymous clinical information about age, sex and primary diagnosis (coxarthrosis or hip fracture). The femoral neck cortex from the inferomedial region was analyzed in a site-matched manner using a combination of micromechanical testing (nanoindentation, micropillar compression) together with micro-CT and quantitative polarized Raman spectroscopy for both morphological and compositional characterization. Mechanical properties, as well as the sample-level mineral density, were constant over age. Only compositional properties demonstrate weak dependence on patient age: decreasing mineral to matrix ratio (p = 0.02, R2 = 0.13, 2.6 % per decade) and increasing amide I sub-peak ratio I∼1660/I∼1683 (p = 0.04, R2 = 0.11, 1.5 % per decade). The patient's sex and diagnosis did not seem to influence investigated bone properties. A clear zonal dependence between interstitial and osteonal cortical zones was observed for compositional and elastic bone properties (p < 0.0001). Site-matched microscale analysis confirmed that all investigated mechanical properties except yield strain demonstrate a positive correlation with the mineral fraction of bone. The output database is the first to integrate the experimentally assessed microscale yield properties, local tissue composition and morphology with the available patient clinical information. The final dataset was used for bone fracture risk prediction in-silico through the principal component analysis and the Naïve Bayes classification algorithm. The analysis showed that the mineral to matrix ratio, indentation hardness and micropillar yield stress are the most relevant parameters for bone fracture risk prediction at 70 % model accuracy (0.71 AUC). Due to the low number of samples, further studies to build a universal fracture prediction algorithm are anticipated with the higher number of patients (N > 200). The proposed classification algorithm together with the output dataset of bone tissue properties can be used for the future comparison of existing methods to evaluate bone quality as well as to form a better understanding of the mechanisms through which bone tissue is affected by aging or disease.

Assessing minipig compact jawbone quality at the microscale.

Preclinical studies often require animal models for in vivo experiments. Particularly in dental research, pig species are extensively used due to their anatomical similarity to humans. However, there is a considerable knowledge gap on the multiscale morphological and mechanical properties of the miniature pigs' jawbones, which is crucial for implant studies and a direct comparison to human tissue. In the present work, we demonstrate a multimodal framework to assess the jawbone quantity and quality for a minipig animal model that could be further extended to humans. Three minipig genotypes, commonly used in dental research, were examined: Yucatan, Göttingen, and Sinclair. Three animals per genotype were tested. Cortical bone samples were extracted from the premolar region of the mandible, opposite to the teeth growth. Global morphological, compositional, and mechanical properties were assessed using micro-computed tomography (micro-CT) together with Raman spectroscopy and nanoindentation measurements, averaged over the sample area. Local mineral-mechanical relationships were investigated with the site-matched Raman spectroscopy and micropillar compression tests. For this, a novel femtosecond laser ablation protocol was developed, allowing high-throughput micropillar fabrication and testing without exposure to high vacuum. At the global averaged sample level, bone relative mineralization demonstrated a significant difference between the genotypes, which was not observed from the complementary micro-CT measurements. Moreover, bone hardness measured by nanoindentation showed a positive trend with the relative mineralization. For all genotypes, significant differences between the relative mineralization and elastic properties were more pronounced within the osteonal regions of cortical bone. Site-matched micropillar compression and Raman spectroscopy highlighted the differences between the genotypes' yield stress and mineral to matrix ratios. The methods used at the global level (averaged over sample area) could be potentially correlated to the medical tools used to assess jawbone toughness and morphology in clinics. On the other hand, the local analysis methods can be applied to quantify compressive bone mechanical properties and their relationship to bone mineralization.

Unified validation of a refined second-generation HR-pQCT based homogenized finite element method to predict strength of the distal segments in radius and tibia.

INTRODUCTION: HR-pQCT based micro finite element (µFE) analyses are considered as "gold standard" for virtual biomechanical analyses of peripheral bone sites such as the distal segment of radius and tibia. An attractive alternative for clinical use is a homogenized finite element method (hFE) based on constitutive models, because of its much shorter evaluation times and modest computational resource requirements. Such hFE models have been experimentally validated for the distal segment of the radius, but neither for the distal segments of the tibia nor for both measurement sites together. Accordingly, the aim of the present study was to refine and experimentally validate an hFE processing pipeline for in vivo prediction of bone strength and stiffness at the distal segments of the radius and the tibia, using only one unified set of material properties. MATERIAL AND METHODS: An existing hFE analysis procedure was refined in several aspects: 1) to include a faster evaluation of material orientation based on the mean surface length (MSL) method, 2) to distinguish cortical and trabecular bone compartments with distinct material properties and 3) to directly superimpose material properties in mixed phase elements instead of densities. Based on an existing dataset of the distal segment of fresh-frozen radii (double sections 20.4 mm, n = 21) and a newly established dataset of the distal segment of fresh-frozen tibiae (triple sections, 30.6 mm, n = 25), a single set of material properties was calibrated on the radius dataset and validated on the tibia dataset by comparing hFE stiffness and ultimate load with respective experimental results, obtained by compressing the samples on a servo-hydraulic testing machine at a monotonic and quasi-static displacement rate up to failure. RESULTS: Using the identified set of material properties, the hFE-predicted stiffness and failure load were in excellent agreement with respective experimental results at both measurement sites (radius stiffness R2 = 0.93, slope = 1.00, intercept = 479 N/mm2/radius ultimate load: R2 = 0.97, slope = 1.00, intercept = 679 N; tibia stiffness R2 = 0.96, slope = 1.01, intercept = -1027 N/mm2/tibia ultimate load: R2 = 0.97, slope = 1.04, intercept = 394 N; combined dataset stiffness R2 = 0.95, slope = 1.01, intercept = -230 N/mm2/combined dataset ultimate load: R2 = 0.97, slope = 1.03, intercept = 495 N). DISCUSSION AND CONCLUSION: In conjunction with unified BV/TV calibration, the established hFE pipeline accurately predicts experimental stiffness and ultimate load of distal multi-sections at the radius and tibia. Processing time for non-linear analysis was substantially reduced compared to previous µFE and hFE methods but could be further minimized by estimating bone strength based on a fast and linear analysis like as is currently done with µ FE.

Fabric-elasticity relationships of tibial trabecular bone are similar in osteogenesis imperfecta and healthy individuals.

Osteogenesis Imperfecta (OI) is an inherited form of bone fragility characterised by impaired synthesis of type I collagen, altered trabecular bone architecture and reduced bone mass. High resolution peripheral computed tomography (HR-pQCT) is a powerful method to investigate bone morphology at peripheral sites including the weight-bearing distal tibia. The resulting 3D reconstructions can be used as a basis of micro-finite element (FE) or homogenized finite element (hFE) models for bone strength estimation. The hFE scheme uses homogenized local bone volume fraction (BV/TV) and anisotropy information (fabric) to compute healthy bone strength within a reasonable computation time using fabric-elasticity relationships. However, it is unclear if these relationships quantified previously for healthy controls are valid for trabecular bone from OI patients. Thus, the aim of this study is to investigate fabric-elasticity relationships in OI trabecular bone compared to healthy controls. In the present study, the morphology of distal tibiae from 50 adults with OI were compared to 120 healthy controls using second generation HR-pQCT. Six cubic regions of interest (ROIs) were selected per individual in a common anatomical region. A first matching between OI and healthy control group was performed by selecting similar individuals to obtain identical mean and median age and sex distribution. It allowed us to perform a first morphometric analysis and compare the outcome with literature. Then, stiffness tensors of the ROIs were computed using µFE and multiple linear regressions were performed with the Zysset-Curnier orthotropic fabric-elasticity model. An initial fit was performed on both the OI group and the healthy control group using all extracted ROIs. Then, data was filtered according to a fixed threshold for a defined coefficient of variation (CV) assessing ROI heterogeneity and additional linear regressions were performed on these filtered data sets. These full and filtered data were in turn compared with previous results from µCT reconstructions obtained in other anatomical locations. Finally, the ROIs of both groups were matched according to their BV/TV and degree of anisotropy (DA). Linear regressions were performed using these matched data to detect statistical differences between the two groups. Compared to healthy controls, we found the OI samples to have significantly lower BV/TV and trabecular number (Tb.N.), significantly higher CV, trabecular separation (Tb.Sp.) and trabecular separation standard deviation (Tb.Sp.SD), but no differences in trabecular thickness (Tb.Th.). These results are in agreement with previous studies. The stiffnesses of highly heterogeneous ROIs were randomly lower with respect to the fabric-elasticity relationships, which reflects the limit of validity of the computational homogenisation methodology. This limitation does not challenge the fabric-elasticity relationship, which extrapolation to heterogeneous ROIs is probably reasonable but can simply not be evaluated with the employed homogenisation methodology. Moreover, due to their low BV/TV, the potential (unknown) errors on these heterogeneous ROIs would have negligible influence on whole bone stiffness in comparison to homogeneous ROIs which are orders of magnitude stiffer. The filtering of highly heterogeneous ROIs removed these low stiffness ROIs and led to similar correlation coefficients for both OI and healthy groups. Finally, the BV/TV and DA matched data revealed no significant differences in fabric-elasticity parameters between OI and healthy individuals. Moreover, the filtering step did not exclude a particular OI type. Compared to previous studies, the stiffness constants from the 61 µm resolution HR-pQCT ROIs were lower than for the 36 µm resolution µCT ROIs. In conclusion, OI trabecular bone of the distal tibia was shown to be significantly more heterogeneous and have a lower BV/TV than healthy controls. Despite the reduced linear regression parameters found for HR-pQCT images, the fabric-elasticity relationships between OI and healthy individuals are similar when the trabecular bone ROIs are sufficiently homogeneous to perform the computational stiffness analysis. Accordingly, the elastic properties used for FEA of healthy bones are also valid for OI bones.

Compressive Strength of Iliac Bone ECM Is Not Reduced in Osteogenesis Imperfecta and Increases With Mineralization.

Osteogenesis imperfecta (OI) is an inheritable, genetic, and collagen-related disorder leading to an increase in bone fragility, but the origin of its "brittle behavior" is unclear. Because of its complex hierarchical structure, bone behaves differently at various length scales. This study aims to compare mechanical properties of human OI bone with healthy control bone at the extracellular matrix (ECM) level and to quantify the influence of the degree of mineralization. Degree of mineralization and mechanical properties were analyzed under dry conditions in 12 fixed and embedded transiliac crest biopsies (control n = 6, OI type I n = 3, OI type IV n = 2, and OI type III n = 1). Mean degree of mineralization was measured by microcomputed tomography at the biopsy level and the mineral-to-matrix ratio was assessed by Raman spectroscopy at the ECM level. Both methods revealed that the degree of mineralization is higher for OI bone compared with healthy control. Micropillar compression is a novel technique for quantifying post-yield properties of bone at the ECM level. Micropillars (d = 5 µm, h = 10 µm) were fabricated using focused ion beam milling and quasi-statically compressed to capture key post-yield properties such as ultimate strength. The qualitative inspection of the stress-strain curves showed that both OI and healthy control bone have a ductile response at the ECM level. The quantitative results showed that compressive strength is not reduced in OI bone and is increasing with OI severity. Nanoindentation measurements revealed that OI bone tends to have a higher Young's modulus, hardness, and dissipated energy compared with healthy bone. Micropillar strength and indentation modulus increased linearly and significantly (p < .0001) with mineral-to-matrix ratio. In conclusion, this study indicates that compressive mechanical properties of dry OI bone at the iliac crest are not inferior to healthy control at the ECM level and increase with mineralization. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Prediction of insertion torque and stiffness of a dental implant in bovine trabecular bone using explicit micro-finite element analysis.

The assessment of dental implant performance is dominated by the concept of mechanical stability. Primary stability is defined as the capacity of a bone-implant structure to bear loads without occurrence of excessive damage and loosening. In order to achieve the highest primary stability, dental implants are inserted into bone using a press-fit procedure. Pre- and postoperative evaluation of primary stability using implantation torque and resonance frequency analysis are valid approaches but do not allow the systematic comparison of different protocols in similar situations. The aim of this research is to develop and validate an explicit, micro-finite element (µFE) methodology to study the effect of different amounts of initial press-fit on implantation torque and initial stiffness of a dental implant. Ten bovine trabecular bone samples were prepared that cover a wide range of bone volume fraction. A dental implant was inserted using two implantation protocols named soft (small initial drilled hole) and dense (increased initial drilled hole). The implantation torque was measured and the stiffness was calculated using an infinitesimal off-axis loading. Finite element simulations of the implant insertion and subsequent loading were performed on micro-computed tomography (µCT) reconstructions of the samples using an explicit solver. Bone was defined as an elasto-plastic material with von Mises yield criteria and hardening. Element deletion was triggered by a threshold in cumulated plastic strains. A sensitivity analysis was performed on friction, hardening and fracture strain to provide a better insight into the effects of these parameters on the results. The implantation torque required for the soft protocol was higher compared to the dense approach in both experiment and simulation due to the higher amount of bone compaction in the first approach. Interestingly, stiffness did not show a significant dependency on the drilling protocol in both experiment and simulation. In conclusion, the explicit microFE methodology developed in this study was able to capture the outcome of two drilling protocols in terms of torque and stiffness and represents a powerful tool to explore the effect of different parameters on primary stability of dental implants.