Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images.

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

Head-Neck Osteoplasty has Minor Effect on the Strength of an Ovine Cam-FAI Model: In Vitro and Finite Element Analyses.

BACKGROUND: Osteochondroplasty of the head-neck region is performed on patients with cam femoroacetabular impingement (FAI) without fully understanding its repercussion on the integrity of the femur. Cam-type FAI can be surgically and reproducibly induced in the ovine femur, which makes it suitable for studying corrective surgery in a consistent way. Finite element models built on quantitative CT (QCT) are computer tools that can be used to predict femoral strength and evaluate the mechanical effect of surgical correction. QUESTIONS/PURPOSES: We asked: (1) What is the effect of a resection of the superolateral aspect of the ovine femoral head-neck junction on failure load? (2) How does the failure load after osteochondroplasty compare with reported forces from activities of daily living in sheep? (3) How do failure loads and failure locations from the computer simulations compare with the experiments? METHODS: Osteochondroplasties (3, 6, 9 mm) were performed on one side of 18 ovine femoral pairs with the contralateral intact side as a control. The 36 femurs were scanned via QCT from which specimen-specific computer models were built. Destructive compression tests then were conducted experimentally using a servohydraulic testing system and numerically via the computer models. Safety factors were calculated as the ratio of the maximal force measured in vivo by telemeterized hip implants during the sheep's walking and running activities to the failure load. The simulated failure loads and failure locations from the computer models were compared with the experimental results. RESULTS: Failure loads were reduced by 5% (95% CI, 2%-8%) for the 3-mm group (p = 0.0089), 10% (95% CI, 6%-14%) for the 6-mm group (p = 0.0015), and 19% (95% CI, 13%-26%) for the 9-mm group (p = 0.0097) compared with the controls. Yet, the weakest specimen still supported more than 2.4 times the peak load during running. Strong correspondence was found between the simulated and experimental failure loads (R2 = 0.83; p < 0.001) and failure locations. CONCLUSIONS: The resistance of ovine femurs to fracture decreased with deeper resections. However, under in vitro testing conditions, the effect on femoral strength remains small even after 9 mm correction, suggesting that femoral head-neck osteochondroplasty could be done safely on the ovine femur. QCT-based finite element models were able to predict weakening of the femur resulting from the osteochondroplasty. CLINICAL RELEVANCE: The ovine femur provides a seemingly safe platform for scientific evaluation of FAI. It also appears that computer models based on preoperative CT scans may have the potential to provide patient-specific guidelines for preventing overcorrection of cam FAI.

Comparison of mixed and kinematic uniform boundary conditions in homogenized elasticity of femoral trabecular bone using microfinite element analyses.

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (lFE) analysis allows computing the apparent elastic properties of trabecular bone for use in homogenized FE (hFE) analysis,but the results depend unfortunately on the type of applied boundary conditions(BCs). In this study, 167 human femoral trabecular cubic regions with a side length of 5.3mm were extracted from three proximal femora and analyzed using lFE analysis to compare systematically their stiffness with kinematic uniform BCs (KUBCs) and periodicity-compatible mixed uniform BCs (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset­Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length (MIL). Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset­Curnier model fitted the apparent elastic constants successfully in both cases with adjusted coefficients of determination (r2adj) of 0.986 for KUBCs and 0.975 for PMUBCs. The proper use of these BCs for hFE analysis of whole bones will need to be investigated in future work.

Experimental validation of finite element analysis of human vertebral collapse under large compressive strains.

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towards the prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Finite element based nonlinear normalization of human lumbar intervertebral disc stiffness to account for its morphology.

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

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.

Influence of mineralization and microporosity on tissue elasticity: experimental and numerical investigation on mineralized turkey leg tendons.

A combined experimental and numerical study correlating indentation stiffness with mineralization and microporosity was performed on mineralized turkey leg tendon. Two distinct tissue morphologies were distinguished by quantitative backscattered electron imaging and called "circumferential" and "interstitial" zones. These two zones showed different tissue organization, microporosity, and mineralization. Stiffness, measured by microindentation, was also different in the two zones. The mean field method of modeling of mineralized collagen fibers was employed to explain the differences.

A patient-specific computer tomography-based finite element methodology to calculate the six dimensional stiffness matrix of human vertebral bodies.

In most finite element (FE) studies of vertebral bodies, axial compression is the loading mode of choice to investigate structural properties, but this might not adequately reflect the various loads to which the spine is subjected during daily activities or the increased fracture risk associated with shearing or bending loads. This work aims at proposing a patient-specific computer tomography (CT)-based methodology, using the currently most advanced, clinically applicable finite element approach to perform a structural investigation of the vertebral body by calculation of its full six dimensional (6D) stiffness matrix. FE models were created from voxel images after smoothing of the peripheral voxels and extrusion of a cortical shell, with material laws describing heterogeneous, anisotropic elasticity for trabecular bone, isotropic elasticity for the cortex based on experimental data. Validated against experimental axial stiffness, these models were loaded in the six canonical modes and their 6D stiffness matrix calculated. Results show that, on average, the major vertebral rigidities correlated well or excellently with the axial rigidity but that weaker correlations were observed for the minor coupling rigidities and for the image-based density measurements. This suggests that axial rigidity is representative of the overall stiffness of the vertebral body and that finite element analysis brings more insight in vertebral fragility than densitometric approaches. Finally, this extended patient-specific FE methodology provides a more complete quantification of structural properties for clinical studies at the spine.

The effect of standard and low-modulus cement augmentation on the stiffness, strength, and endplate pressure distribution in vertebroplasty.

PURPOSE: Vertebroplasty restores stiffness and strength of fractured vertebral bodies, but alters their stress transfer. This unwanted effect may be reduced by using more compliant cements. However, systematic experimental comparison of structural properties between standard and low-modulus augmentation needs to be done. This study investigated how standard and low-modulus cement augmentation affects apparent stiffness, strength, and endplate pressure distribution of vertebral body sections. METHODS: Thirty-nine human thoracolumbar vertebral body sections were prepared by removing cortical endplates and posterior elements. The specimens were scanned with a HR-pQCT system and loaded in the elastic range. After augmentation with standard or low-modulus cement they were scanned again and tested in two steps. First, the contact pressure distribution between specimen and loading plates was measured with pressure-sensitive films. Then, they were loaded again in the elastic range and compressed until failure. Apparent stiffness was compared before and after augmentation, whereas apparent strength of augmented specimens was compared to a non-augmented reference group. RESULTS: Vertebral body sections with fillings connecting both endplates were on average 33% stiffer and 47% stronger with standard cement, and 27% stiffer and 30% stronger with low-modulus cement. In contrast, partial fillings showed no significant strengthening for both cements and only a slight stiffness increase (<16%). The averaged endplate pressure above/below the cement was on average 15% lower with low-modulus cement compared to standard cement. CONCLUSION: Augmentation connecting both endplates significantly strengthened and stiffened vertebral body sections also with low-modulus cement. A trend of reduced pressure concentrations above/below the cement was observed with low-modulus cement.

Assessment of a novel biomechanical fracture model for distal radius fractures.

BACKGROUND: Distal radius fractures (DRF) are one of the most common fractures and often need surgical treatment, which has been validated through biomechanical tests. Currently a number of different fracture models are used, none of which resemble the in vivo fracture location. The aim of the study was to develop a new standardized fracture model for DRF (AO-23.A3) and compare its biomechanical behavior to the current gold standard. METHODS: Variable angle locking volar plates (ADAPTIVE, Medartis) were mounted on 10 pairs of fresh-frozen radii. The osteotomy location was alternated within each pair (New: 10 mm wedge 8 mm / 12 mm proximal to the dorsal / volar apex of the articular surface; Gold standard: 10 mm wedge 20 mm proximal to the articular surface). Each specimen was tested in cyclic axial compression (increasing load by 100 N per cycle) until failure or -3 mm displacement. Parameters assessed were stiffness, displacement and dissipated work calculated for each cycle and ultimate load. Significance was tested using a linear mixed model and Wald test as well as t-tests. RESULTS: 7 female and 3 male pairs of radii aged 74 ± 9 years were tested. In most cases (7/10), the two groups showed similar mechanical behavior at low loads with increasing differences at increasing loads. Overall the novel fracture model showed a significant different biomechanical behavior than the gold standard model (p < 0,001). The average final loads resisted were significantly lower in the novel model (860 N ± 232 N vs. 1250 N ± 341 N; p = 0.001). CONCLUSION: The novel biomechanical fracture model for DRF more closely mimics the in vivo fracture site and shows a significantly different biomechanical behavior with increasing loads when compared to the current gold standard.

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.

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.

A quantitative collagen fibers orientation assessment using birefringence measurements: calibration and application to human osteons.

Even though mechanical properties depend strongly on the arrangement of collagen fibers in mineralized tissues, it is not yet well resolved. Only a few semi-quantitative evaluations of the fiber arrangement in bone, like spectroscopic techniques or circularly polarized light microscopy methods are available. In this study the out-of-plane collagen arrangement angle was calibrated to the linear birefringence of a longitudinally fibered mineralized turkey leg tendon cut at variety of angles to the main axis. The calibration curve was applied to human cortical bone osteons to quantify the out-of-plane collagen fibers arrangement. The proposed calibration curve is normalized to sample thickness and wavelength of the probing light to enable a universally applicable quantitative assessment. This approach may improve our understanding of the fibrillar structure of bone and its implications on mechanical properties.

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.

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.

The role of fabric in the large strain compressive behavior of human trabecular bone.

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (∼70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.

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.

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.