In situ synchrotron radiation µCT indentation of cortical bone: Anisotropic crack propagation, local deformation, and fracture.

The development of treatment strategies for skeletal diseases relies on the understanding of bone mechanical properties in relation to its structure at different length scales. At the microscale, indention techniques can be used to evaluate the elastic, plastic, and fracture behaviour of bone tissue. Here, we combined in situ high-resolution SRµCT indentation testing and digital volume correlation to elucidate the anisotropic crack propagation, deformation, and fracture of ovine cortical bone under Berkovich and spherical tips. Independently of the indenter type we observed significant dependence of the crack development due to the anisotropy ahead of the tip, with lower strains and smaller crack systems developing in samples indented in the transverse material direction, where the fibrillar bone ultrastructure is largely aligned perpendicular to the indentation direction. Such alignment allows to accommodate the strain energy, inhibiting crack propagation. Higher tensile hoop strains generally correlated with regions that display significant cracking radial to the indenter, indicating a predominant Mode I fracture. This was confirmed by the three-dimensional analysis of crack opening displacements and stress intensity factors along the crack front obtained for the first time from full displacement fields in bone tissue. The X-ray beam significantly influenced the relaxation behaviour independent of the tip. Raman analyses did not show significant changes in specimen composition after irradiation compared to non-irradiated tissue, suggesting an embrittlement process that may be linked to damage of the non-fibrillar organic matrix. This study highlights the importance of three-dimensional investigation of bone deformation and fracture behaviour to explore the mechanisms of bone failure in relation to structural changes due to ageing or disease. STATEMENT OF SIGNIFICANCE: Characterising the three-dimensional deformation and fracture behaviour of bone remains essential to decipher the interplay between structure, function, and composition with the aim to improve fracture prevention strategies. The experimental methodology presented here, combining high-resolution imaging, indentation testing and digital volume correlation, allows us to quantify the local deformation, crack propagation, and fracture modes of cortical bone tissue. Our results highlight the anisotropic behaviour of osteonal bone and the complex crack propagation patterns and fracture modes initiating by the intricate stress states beneath the indenter tip. This is of wide interest not only for the understanding of bone fracture but also to understand other architectured (bio)structures providing an effective way to quantify their toughening mechanisms in relation to their main mechanical function.

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres.

The hierarchical design of bio-based nanostructured materials such as bone enables them to combine unique structure-mechanical properties. As one of its main components, water plays an important role in bone's material multiscale mechanical interplay. However, its influence has not been quantified at the length-scale of a mineralised collagen fibre. Here, we couple in situ micropillar compression, and simultaneous synchrotron small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) with a statistical constitutive model. Since the synchrotron data contain statistical information on the nanostructure, we establish a direct connection between experiment and model to identify the rehydrated elasto-plastic micro- and nanomechanical fibre behaviour. Rehydration led to a decrease of 65%-75% in fibre yield stress and compressive strength, and 70% in stiffness with a 3x higher effect on stresses than strains. While in agreement with bone extracellular matrix, the decrease is 1.5-3x higher compared to micro-indentation and macro-compression. Hydration influences mineral more than fibril strain with the highest difference to the macroscale when comparing mineral and tissue levels. The effect of hydration seems to be strongly mediated by ultrastructural interfaces while results provide insights towards mechanical consequences of reported water-mediated structuring of bone apatite. The missing reinforcing capacity of surrounding tissue for an excised fibril array is more pronounced in wet than dry conditions, mainly related to fibril swelling. Differences leading to higher compressive strength between mineralised tissues seem not to depend on rehydration while the lack of kink bands supports the role of water as an elastic embedding influencing energy-absorption mechanisms. STATEMENT OF SIGNIFICANCE: Characterising structure-property-function relationships in hierarchical biological materials helps us to elucidate mechanisms that enable their unique properties. Experimental and computational methods can advance our understanding of their complex behaviour with the potential to inform bio-inspired material development. In this study, we close a gap for bone's fundamental mechanical building block at micro- and nanometre length scales. We establish a direct connection between experiments and simulations by coupling in situ synchrotron tests with a statistical model and quantify the behaviour of rehydrated single mineralised collagen fibres. Results suggest a high influence of hydration on structural interfaces, and the role of water as an elastic embedding by outlining important differences between wet and dry elasto-plastic properties of mineral nanocrystals, fibrils and fibres.

Evaluation of Load-To-Strength Ratios in Metastatic Vertebrae and Comparison With Age- and Sex-Matched Healthy Individuals.

Vertebrae containing osteolytic and osteosclerotic bone metastases undergo pathologic vertebral fracture (PVF) when the lesioned vertebrae fail to carry daily loads. We hypothesize that task-specific spinal loading patterns amplify the risk of PVF, with a higher degree of risk in osteolytic than in osteosclerotic vertebrae. To test this hypothesis, we obtained clinical CT images of 11 cadaveric spines with bone metastases, estimated the individual vertebral strength from the CT data, and created spine-specific musculoskeletal models from the CT data. We established a musculoskeletal model for each spine to compute vertebral loading for natural standing, natural standing + weights, forward flexion + weights, and lateral bending + weights and derived the individual vertebral load-to-strength ratio (LSR). For each activity, we compared the metastatic spines' predicted LSRs with the normative LSRs generated from a population-based sample of 250 men and women of comparable ages. Bone metastases classification significantly affected the CT-estimated vertebral strength (Kruskal-Wallis, p < 0.0001). Post-test analysis showed that the estimated vertebral strength of osteosclerotic and mixed metastases vertebrae was significantly higher than that of osteolytic vertebrae (p = 0.0016 and p = 0.0003) or vertebrae without radiographic evidence of bone metastasis (p = 0.0010 and p = 0.0003). Compared with the median (50%) LSRs of the normative dataset, osteolytic vertebrae had higher median (50%) LSRs under natural standing (p = 0.0375), natural standing + weights (p = 0.0118), and lateral bending + weights (p = 0.0111). Surprisingly, vertebrae showing minimal radiographic evidence of bone metastasis presented significantly higher median (50%) LSRs under natural standing (p < 0.0001) and lateral bending + weights (p = 0.0009) than the normative dataset. Osteosclerotic vertebrae had lower median (50%) LSRs under natural standing (p < 0.0001), natural standing + weights (p = 0.0005), forward flexion + weights (p < 0.0001), and lateral bending + weights (p = 0.0002), a trend shared by vertebrae with mixed lesions. This study is the first to apply musculoskeletal modeling to estimate individual vertebral loading in pathologic spines and highlights the role of task-specific loading in augmenting PVF risk associated with specific bone metastatic types. Our finding of high LSRs in vertebrae without radiologically observed bone metastasis highlights that patients with metastatic spine disease could be at an increased risk of vertebral fractures even at levels where lesions have not been identified radiologically.

Influence of Metastatic Bone Lesion Type and Tumor Origin on Human Vertebral Bone Architecture, Matrix Quality, and Mechanical Properties.

Metastatic spine disease is incurable, causing increased vertebral fracture risk and severe patient morbidity. Here, we demonstrate that osteolytic, osteosclerotic, and mixed bone metastasis uniquely modify human vertebral bone architecture and quality, affecting vertebral strength and stiffness. Multivariable analysis showed bone metastasis type dominates vertebral strength and stiffness changes, with neither age nor gender having an independent effect. In osteolytic vertebrae, bone architecture rarefaction, lower tissue mineral content and connectivity, and accumulation of advanced glycation end-products (AGEs) affected low vertebral strength and stiffness. In osteosclerotic vertebrae, high trabecular number and thickness but low AGEs, suggesting a high degree of bone remodeling, yielded high vertebral strength. Our study found that bone metastasis from prostate and breast primary cancers differentially impacted the osteosclerotic bone microenvironment, yielding altered bone architecture and accumulation of AGEs. These findings indicate that therapeutic approaches should target the restoration of bone structural integrity. © 2022 American Society for Bone and Mineral Research (ASBMR).

Non-linear explicit micro-FE models accurately predict axial pull-out force of cortical screws in human tibial cortical bone.

Screws are the most frequently used implants for treatment of bone fractures and play an essential role in determining fixation stability. Robust prediction of the bone-screw interface failure would enable development of improved fixation strategies and implant designs, ultimately reducing failure rates and improving outcomes of bone fracture treatments. This study aimed to compare the accuracy of micro-computed tomography image based bone volume measures, linear micro-finite element (FE) and non-linear micro-FE simulations in predicting pull-out force of 3.5 mm screws in human cadaveric tibial cortical bone. Axial pull-out experiments were performed in forty samples harvested from a single human tibia to measure ultimate force, which was correlated with bone volume around the screw and the predictions by both linear micro-FE and non-linear explicit micro-FE models. Correlation strength was similar for bone volume around the screw (R2 = 0.866) and linear micro-FE (R2 = 0.861), but the explicit non-linear micro-FE models were able to capture the experimental results more accurately (R2 = 0.913) and quantitatively correctly. Therefore, this technique may have potential for future in silico studies aiming at implant design optimization.

An experimentally informed statistical elasto-plastic mineralised collagen fibre model at the micrometre and nanometre lengthscale.

Bone is an intriguingly complex material. It combines high strength, toughness and lightweight via an elaborate hierarchical structure. This structure results from a biologically driven self-assembly and self-organisation, and leads to different deformation mechanisms along the length scales. Characterising multiscale bone mechanics is fundamental to better understand these mechanisms including changes due to bone-related diseases. It also guides us in the design of new bio-inspired materials. A key-gap in understanding bone's behaviour exists for its fundamental mechanical unit, the mineralised collagen fibre, a composite of organic collagen molecules and inorganic mineral nanocrystals. Here, we report an experimentally informed statistical elasto-plastic model to explain the fibre behaviour including the nanoscale interplay and load transfer with its main mechanical components. We utilise data from synchrotron nanoscale imaging, and combined micropillar compression and synchrotron X-ray scattering to develop the model. We see that a 10-15% micro- and nanomechanical heterogeneity in mechanical properties is essential to promote the ductile microscale behaviour preventing an abrupt overall failure even when individual fibrils have failed. We see that mineral particles take up 45% of strain compared to collagen molecules while interfibrillar shearing seems to enable the ductile post-yield behaviour. Our results suggest that a change in mineralisation and fibril-to-matrix interaction leads to different mechanical properties among mineralised tissues. Our model operates at crystalline-, molecular- and continuum-levels and sheds light on the micro- and nanoscale deformation of fibril-matrix reinforced composites.

Prediction of the Inelastic Behaviour of Radius Segments: Damage-based Nonlinear Micro Finite Element Simulation vs Pistoia Criterion.

The Pistoia criterion (PC) is widely used to estimate the failure load of distal radius segments based on linear micro Finite Element (µFE) analyses. The advantage of the PC is that a simple strain-threshold and a tissue volume fraction can be used to predict failure properties. In this study, the PC is compared to materially nonlinear µFE analyses, where the bone tissue is modelled as an elastic, damageable material. The goal was to investigate for which outcomes the PC is sufficient and when a nonlinear (NL) simulation is required. Three types of simulation results were compared: (1) prediction of the failure load, (2) load sharing of cortical and trabecular regions, and (3) distribution of local damaged/overstrained tissue at the maximum sustainable load. The failure load obtained experimentally could be predicted well with both the PC and the NL simulations using linear regression. Although the PC strongly overestimated the failure load, it was sufficient to predict adequately normalized apparent results. An optimised PC (oPC) was proposed which uses experimental data to calibrate the individual volume of overstrained tissue. The main areas of local over-straining predicted by the oPC were the same as estimated by the NL simulation, although the oPC predicted more diffuse regions. However, the oPC relied on an individual calibration requiring the experimental failure load while the NL simulation required no a priori knowledge of the experimental failure load.

Empirical relationships between bone density and ultimate strength: A literature review.

INTRODUCTION: Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites. METHODS: All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships. RESULTS: Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone. CONCLUSIONS: Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Conventional finite element models estimate the strength of metastatic human vertebrae despite alterations of the bone's tissue and structure.

INTRODUCTION: Pathologic vertebral fractures are a major clinical concern in the management of cancer patients with metastatic spine disease. These fractures are a direct consequence of the effect of bone metastases on the anatomy and structure of the vertebral bone. The goals of this study were twofold. First, we evaluated the effect of lytic, blastic and mixed (both lytic and blastic) metastases on the bone structure, on its material properties, and on the overall vertebral strength. Second, we tested the ability of bone mineral content (BMC) measurements and standard FE methodologies to predict the strength of real metastatic vertebral bodies. METHODS: Fifty-seven vertebral bodies from eleven cadaver spines containing lytic, blastic, and mixed metastatic lesions from donors with breast, esophageal, kidney, lung, or prostate cancer were scanned using micro-computed tomography (µCT). Based on radiographic review, twelve vertebrae were selected for nanoindentation testing, while the remaining forty-five vertebrae were used for assessing their compressive strength. The µCT reconstruction was exploited to measure the vertebral BMC and to establish two finite element models. 1) a micro finite element (µFE) model derived at an image resolution of 24.5 µm and 2) homogenized FE (hFE) model derived at a resolution of 0.98 mm. Statistical analyses were conducted to measure the effect of the bone metastases on BV/TV, indentation modulus (Eit), ratio of plastic/total work (WPl/Wtot), and in vitro vertebral strength (Fexp). The predictive value of BMC, µFE stiffness, and hFE strength were evaluated against the in vitro measurements. RESULTS: Blastic vertebral bodies exhibit significantly higher BV/TV compared to the mixed (p = 0.0205) and lytic (p = 0.0216) vertebral bodies. No significant differences were found between lytic and mixed vertebrae (p = 0.7584). Blastic bone tissue exhibited a 5.8% lower median Eit (p< 0.001) and a 3.3% lower median Wpl/Wtot (p<0.001) compared to non-involved bone tissue. No significant differences were measured between lytic and non-involved bone tissues. Fexp ranged from 1.9 to 13.8 kN, was strongly associated with hFE strength (R2=0.78, p< 0.001) and moderately associated with BMC (R2=0.66, p< 0.001) and µFE stiffness (R2=0.66, p< 0.001), independently of the lesion type. DISCUSSION: Our findings show that tumour-induced osteoblastic metastases lead to slightly, but significantly lower bone tissue properties compared to controls, while osteolytic lesions appear to have a negligible impact. These effects may be attributed to the lower mineralization and woven nature of bone forming in blastic lesions whilst the material properties of bone in osteolytic vertebrae appeared little changed. The moderate association between BMC- and FE-based predictions to fracture strength suggest that vertebral strength is affected by the changes of bone mass induced by the metastatic lesions, rather than altered tissue properties. In a broader context, standard hFE approaches generated from CTs at clinical resolution are robust to the lesion type when predicting vertebral strength. These findings open the door for the development of FE-based prediction tools that overcomes the limitations of BMC in accounting for shape and size of the metastatic lesions. Such tools may help clinicians to decide whether a patient needs the prophylactic fixation of an impending fracture.

Explicit finite element analysis can predict the mechanical response of conical implant press-fit in homogenized trabecular bone.

Prediction of primary stability is a major challenge in the surgical planning of dental and orthopedic implants. Computational methods become attractive to estimate primary stability from clinical CT images, but implicit finite element analysis of implant press-fit faces convergence issues due to contact and highly distorted elements. This study aims to develop and validate an explicit finite element method to simulate the insertion and primary stability of a rigid implant in a deformable bone while accounting for damage occurring at the bone-implant interface. Accordingly, a press-fit experiment of a conical implant into predrilled bovine trabecular bone was designed and realized for six samples. A displacement-driven cyclic protocol was used to quantify the reaction force and stiffness of the bone-implant system. Homogenized finite element analyses of the experiments were performed by modeling contact with friction and converting an existing constitutive model with elasto-plasticity and damage of bone tissue to be applicable to an explicit time integration scheme where highly distorted elements get deleted. The computed reaction forces and unloading stiffnesses showed high correlations (R2 = 0.95 and R2 = 0.94) with the experiment. Friction between bone and implant exhibited a strong influence on both reaction force and stiffness. In conclusion, the developed explicit finite element approach with frictional contact and element deletion accounts properly for bone damage during press-fit and will help optimizing dental or orthopedic implant design towards maximal primary stability.

Finite element models can reproduce the effect of nucleotomy on the multi-axial compliance of human intervertebral discs.

Finite element (FE) models can unravel the link between intervertebral disc (IVD) degeneration and its mechanical behaviour. Nucleotomy may provide the data required for model verification. Three human IVDs were scanned with MRI and tested in multiple loading scenarios, prior and post nucleotomy. The resulting data was used to generate, calibrate, and verify the FE models. Nucleotomy increased the experimental range of motion by 26%, a result reproduced by the FE simulation within a 5% error. This work demonstrates the ability of FE models to reproduce the mechanical compliance of human IVDs prior and post nucleotomy.

Finite element analysis of bone strength in osteogenesis imperfecta.

As a dedicated experimentalist, John Currey praised the high potential of finite element (FE) analysis but also recognized its critical limitations. The application of the FE methodology to bone tissue is reviewed in the light of his enthusiastic and colorful statements. In the past decades, FE analysis contributed substantially to the understanding of structure-function properties in the hierarchical organization of bone and to the simulation of bone adaptation. The systematic experimental validation of FE analysis of bone strength in anatomical locations at risk of fracture led to its application in clinical studies to evaluate efficacy of antiresorptive or anabolic treatment of bone fragility. Beyond the successful analyses of healthy or osteoporotic bone, FE analysis becomes increasingly involved in the investigation of other fragility-related bone diseases. The case of osteogenesis imperfecta (OI) is exposed, the multiscale alterations of the bone tissue and the effect of treatment summarized. A few FE analyses attempting to answer open questions in OI are then reported. An original study is finally presented that explored the structural properties of the Brtl/+ murine model of OI type IV subjected to sclerostin neutralizing antibody treatment using microFE analysis. The use of identical material properties in the four-point bending FE simulations of the femora reproduced not only the experimental values but also the statistical comparisons examining the effect of disease and treatment. Further efforts are needed to build upon the extraordinary legacy of John Currey and clarify the impact of different bone diseases on the hierarchical mechanical properties of bone.

Efficient materially nonlinear [Formula: see text]FE solver for simulations of trabecular bone failure.

An efficient solver for large-scale linear [Formula: see text] simulations was extended for nonlinear material behavior. The material model included damage-based tissue degradation and fracture. The new framework was applied to 20 trabecular biopsies with a mesh resolution of [Formula: see text]. Suitable material parameters were identified based on two biopsies by comparison with axial tension and compression experiments. The good parallel performance and low memory footprint of the solver were preserved. Excellent correlation of the maximum apparent stress was found between simulations and experiments ([Formula: see text]). The development of local damage regions was observable due to the nonlinear nature of the simulations. A novel elasticity limit was proposed based on the local damage information. The elasticity limit was found to be lower than the 0.2% yield point. Systematic differences in the yield behavior of biopsies under apparent compression and tension loading were observed. This indicates that damage distributions could lead to more insight into the failure mechanisms of trabecular bone.

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.

Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro- and nanoscale.

The increasing incidence of osteoporotic bone fractures makes fracture risk prediction an important clinical challenge. Computational models can be utilised to facilitate such analyses. However, they critically depend on bone's underlying hierarchical material description. To understand bone's irreversible behaviour at the micro- and nanoscale, we developed an in situ testing protocol that allows us to directly relate the experimental data to the mechanical behaviour of individual mineralised collagen fibres and its main constitutive phases, the mineralised collagen fibrils and the mineral nanocrystals, by combining micropillar compression of single fibres with small angle X-ray scattering (SAXS) and X-ray diffraction (XRD). Failure modes were assessed by SEM. Strain ratios in the elastic region at fibre, fibril and mineral levels were found to be approximately 22:5:2 with strain ratios at the point of compressive strength of 0.23 ±â€¯0.11 for fibril-to-fibre and 0.07 ±â€¯0.01 for mineral-to-fibre levels. Mineral-to-fibre levels showed highest strain ratios around the apparent yield point, fibril-to-fibre around apparent strength. The mineralised collagen fibrils showed a delayed mechanical response, contrary to the mineral phase, which points towards preceding deformations of mineral nanocrystals in the extrafibrillar matrix. No damage was measured at the level of the mineralised collagen fibre which indicates an incomplete separation of the mineral and collagen, and an extrafibrillar interface failure. The formation of kink bands and the gradual recruitment of fibrils upon compressive loading presumably led to localised strains. Our results from a well-controlled fibrillar architecture provide valuable input for micromechanical models and computational non-linear bone strength analyses that may provide further insights for personalised diagnosis and treatment as well as bio-inspired implants for patients with bone diseases. STATEMENT OF SIGNIFICANCE: Musculoskeletal diseases such as osteoporosis, osteoarthritis or bone cancer significantly challenge health care systems and make fracture risk prediction and treatment optimisation important clinical goals. Computational methods such as finite element models have the potential to optimise analyses but highly depend on underlying material descriptions. We developed an in situ testing set-up to directly relate experimental data to the mechanical behaviour of bone's fundamental building block, the individual mineralised collagen fibre and its main constituents. Low multilevel strain ratios suggest high deformations in the extrafibrillar matrix and energy dissipation at the interfaces, the absence of damage indicates both an incomplete separation between mineral and collagen and an extrafibrillar interface failure. The formation of kink bands in the fibril-reinforced composite presumably led to localised strains. The deformation behaviour of a well-controlled fibrillar architecture provides valuable input for non-linear bone strength analyses.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations.

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (µFE) analyses of trabecular bone. The objective of this study is to explore an explicit µFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using µFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

"Peroperative estimation of bone quality and primary dental implant stability".

OBJECTIVES: Dental implants are widely used to restore function and appearance. It may be essential to choose the appropriate drilling protocol and implant design in order to optimise primary stability. This could be achieved based on an assessment of the implantation site with respect to bone quality and objective biomechanical descriptors such as stiffness and strength of the bone-implant system. The aim of this ex vivo study is to relate these descriptors with bone quality, with a pre-implantation indicator of implant stability: pilot-hole drilling force (Fdrilling), and with two post-implantation indicators: maximal implantation torque (Timplantation) and resonance frequency analysis (RFA). METHODS: Eighty trabecular bone specimens were cored from human vertebrae and bovine tibiae. Bone volume fraction (BV/TV), a representative for bone quality, was obtained through micro-computed tomography scans. Implants were kept in controlled laboratory conditions following standard surgical procedures. Forces and torques were recorded and RFA was assessed after implantation. Off-axis compression tests were conducted on the implants until failure. Implant stability was identified by stiffness and ultimate force (Fultimate). The relationships between BV/TV, Stiffness, Fultimate and Fdrilling, Timplantation, RFA were established. RESULTS: Fdrilling correlated well with BV/TV of the implantation site (r2 = 0.81), stiffness (r2 = 0.75) and Fultimate (r2 = 0.80). Timplantation correlated better with stiffness (r2 = 0.86) and Fultimate (r2 = 0.94) than RFA (r2 = 0.77 and r2 = 0.74, respectively). CONCLUSION: Our results indicate that BV/TV and bone-implant stability can be directly estimated by the force needed for the pilot drilling that occurs during the site preparation before implantation. Moreover, implantation torque outperforms RFA for evaluating the mechanical competence of the bone-implant system.

Integrating MRI-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc.

Intervertebral disc degeneration is a common disease that is often related to impaired mechanical function, herniations and chronic back pain. The degenerative process induces alterations of the disc's shape, composition and structure that can be visualized in vivo using magnetic resonance imaging (MRI). Numerical tools such as finite element analysis (FEA) have the potential to relate MRI-based information to the altered mechanical behavior of the disc. However, in terms of geometry, composition and fiber architecture, current FE models rely on observations made on healthy discs and might therefore not be well suited to study the degeneration process. To address the issue, we propose a new, more realistic FE methodology based on diffusion tensor imaging (DTI). For this study, a human disc joint was imaged in a high-field MR scanner with proton-density weighted (PD) and DTI sequences. The PD image was segmented and an anatomy-specific mesh was generated. Assuming accordance between local principal diffusion direction and local mean collagen fiber alignment, corresponding fiber angles were assigned to each element. Those element-wise fiber directions and PD intensities allowed the homogenized model to smoothly account for composition and fibrous structure of the disc. The disc's in vitro mechanical behavior was quantified under tension, compression, flexion, extension, lateral bending and rotation. The six resulting load-displacement curves could be replicated by the FE model, which supports our approach as a first proof of concept towards patient-specific disc modeling.

Ultimate force and stiffness of 2-piece zirconium dioxide implants with screw-retained monolithic lithium-disilicate reconstructions.

PURPOSE: The aims were to analyze stiffness, ultimate force, and failure modes of a 2-piece zirconium dioxide (ZrO2) implant system. METHODS: Eleven 2-piece ZrO2 implants, each mounted with ZrO2 abutments plus bonded monolithic lithium disilicate (LS2) restorations, were grouped for 3.3mm (A) and 4.1mm (B) diameter samples. Quasi-static load was monotonically applied under a standardized test set-up (loading configuration according to DIN ISO 14801). The ultimate force was defined as the maximum force that implants are able to carry out until fracture; stiffness was measured as the maximum slope during loading. An unpaired t-test was performed between group A and B for ultimate force and stiffness (p<0.05). RESULTS: Force-displacement curves revealed statistically homogenous inner-group results for all samples. Failure modes showed characteristic fractures at the neck configuration of the implants independent of the diameter. Mean stiffness was 1099N/mm (±192) for group A, and significantly lower compared to group B with 1630N/mm (±274) (p<0.01); whereas mean ultimate force was 348N (±53) for group A, and significantly increased for group B with 684N (±29) (p<0.0001). CONCLUSIONS: The examined 2-piece ZrO2 implant system mounted to LS2-restorations seems to be a stable unit under in-vitro conditions with mechanical properties compared to loading capacity of physiological force. The metal-free implant reconstructions demonstrated high stiffness and ultimate force under quasi-static load for single tooth replacement under consideration of the dental indication of narrow and standard diameter implants.

A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage.

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression.