Micro-CT finite element model and experimental validation of trabecular bone damage and fracture

Factual observations of dynamic bone crushing

Dynamic bone-crushing, exemplified by the pig bone rib, is characterized thermo-mechanically in relation to the bone's microstructural characteristics. The cortical bone's dominant role consists of shielding the trabecular component by resisting deformation, sustaining high load levels, and ultimately cracking. Here we present a qualitative factual study to show that this behavior is the absolute opposite of its quasi-static counterpart in which the trabecular bone was found to play the dominant role. Using infrared thermography, we observed for the first time a significant localized temperature rise of up to 11 degrees Celsius in both cortical and trabecular damaging regions. Such observations call for additional clinically oriented research. Such a high contrast between static and dynamic failure mechanisms was not reported previously, and it paves the way for forensic-oriented studies in which the nature of the sustained load must be determined.

Estimation of the in-plane ultimate stress of lamellar tissue as a function of bone mineral density and osteocyte lacunae porosity

BACKGROUND AND OBJECTIVE

Detailed finite element models based on medical images (μ-CT) are commonly used to analyze the mechanical behavior of bone at microscale. In order to simulate the tissue failure onset, isotropic failure criteria of lamellar tissue are often used, despite its non-isotropic and heterogeneous nature. The main goal of the present work is to estimate the in-plane ultimate stress of lamellar bone, considering the influence of mineral content and the porosity due to the osteocyte lacunae concentration.

METHODS

To this aim, a representative volume cell of lamellar tissue is modeled numerically, including: (1) non-isotropic elastic properties of tissue as a function of the bone mineral density and (2) explicit modeling of the osteocyte lacunae, considering the range of porosity content, size and orientation of ellipsoid-shaped lacunae. Firstly, the element size for the finite element models have been defined from a preliminary convergence analysis. Bounds on the ultimate stress of non-porous lamellar tissue are estimated for two values of bone mineral density, considering the results of tensile and compressive tests of wet osteons from the literature. Subsequently, the ultimate stress of lamellar tissue considering several values of micro-porosity is addressed.

RESULTS

Results obtained in this work show that the strength of lamellar bone decreases exponentially with the increase of lacunae porosity concentration. Ultimate stress of non-porous tissue (p=0%) increases with high mineral content, reaching a value of S¯transc=355.40±39.80 MPa for compression in the transversal direction of the fiber bundles, being BMD=1.246g/cm3. The mean value for the longitudinal to transverse strength ratio evaluated for porosity p=0%,1% and 5% and a mineral content BMD=1.2g/cm3, is 2.47:1 for tension and 1.55:1 for compression. These values are in agreement with literature.

CONCLUSIONS

Osteocyte lacunae act as stress concentrators, acting as potential stimulus for the bone regeneration process. A novel micromechanical model for the in-plane ultimate stress of lamellar tissue as a function of mineral content and lacunae concentration is presented. Additional considerations about the intralamellar shear stress evolution are also given.

Prediction of the critical energy release rate for rat femoral cortical bone structure under different failure conditions

BACKGROUND AND OBJECTIVE

Critical energy release rate is a global fracture parameter that could be measured during the failing process, and its value may change under different failure conditions even in the same bone structure. The aim of this study was to propose an approach that combined the experimental test and finite element analysis to predict the critical energy release rates in the femoral cortical bone structures under compression and three-point bending loads.

METHODS

Three-point bending and compression experiments and the corresponding fracture simulations were performed on the rat femoral cortical bone structures. Different values of energy release rate were repeatedly assigned to the finite element models to perform fracture simulations, and then the load-displacement curves predicted in each simulation were compared with the experimental data to back-calculate the critical energy release rate.

RESULTS

The predicted data were similar to the experimental results when the calibrated energy release rate was suitable. The results showed that the cortical bone structure occurred shear open failure under compression load, and the predicted critical energy release rate was 0.12 N/mm. The same cortical bone structure occurred tensile open failure under three-point bending load, and the predicted critical energy release rate was 0.16 N/mm.

CONCLUSIONS

The critical energy release rates were different under various failure conditions in one cortical bone structure. A comprehensive analysis from the perspectives of material mechanical properties, failure mode, and damage fracture mechanism was conducted to reveal the reasons for the differences in the critical energy release rate in the cortical bone structure, which provided a theoretical basis for the measurement of the critical energy release rate and the accurate fracture simulation.

Characterization of mechanical stiffness using additive manufacturing and finite element analysis: potential tool for bone health assessment

BACKGROUND

Bone health and fracture risk are known to be correlated with stiffness. Both micro-finite element analysis (μFEA) and mechanical testing of additive manufactured phantoms are useful approaches for estimating mechanical properties of trabecular bone-like structures. However, it is unclear if measurements from the two approaches are consistent. The purpose of this work is to evaluate the agreement between stiffness measurements obtained from mechanical testing of additive manufactured trabecular bone phantoms and μFEA modeling. Agreement between the two methods would suggest 3D printing is a viable method for validation of μFEA modeling.

METHODS

A set of 20 lumbar vertebrae regions of interests were segmented and the corresponding trabecular bone phantoms were produced using selective laser sintering. The phantoms were mechanically tested in uniaxial compression to derive their stiffness values. The stiffness values were also derived from in silico simulation, where linear elastic μFEA was applied to simulate the same compression and boundary conditions. Bland-Altman analysis was used to evaluate agreement between the mechanical testing and μFEA simulation values. Additionally, we evaluated the fidelity of the 3D printed phantoms as well as the repeatability of the 3D printing and mechanical testing process.

RESULTS

We observed good agreement between the mechanically tested stiffness and μFEA stiffness, with R2 of 0.84 and normalized root mean square deviation of 8.1%. We demonstrate that the overall trabecular bone structures are printed in high fidelity (Dice score of 0.97 (95% CI, [0.96,0.98]) and that mechanical testing is repeatable (coefficient of variation less than 5% for stiffness values from testing of duplicated phantoms). However, we noticed some defects in the resin microstructure of the 3D printed phantoms, which may account for the discrepancy between the stiffness values from simulation and mechanical testing.

CONCLUSION

Overall, the level of agreement achieved between the mechanical stiffness and μFEA indicates that our μFEA methods may be acceptable for assessing bone mechanics of complex trabecular structures as part of an analysis of overall bone health.

An integrated experimental-computational framework to assess the influence of microstructure and material properties on fracture toughness in clinical specimens of human femoral cortical bone

Microstructural and compositional changes that occur due to aging, pathological conditions, or pharmacological treatments alter cortical bone fracture resistance. However, the relative importance of these changes to the fracture resistance of cortical bone has not been quantified in detail. In this technical note, we developed an integrated experimental-computational framework utilizing human femoral cortical bone biopsies to advance the understanding of how fracture resistance of cortical bone is modulated due to modifications in its microstructure and material properties. Four human biopsy samples from individuals with varying fragility fracture history and osteoporosis treatment status were converted to finite element models incorporating specimen-specific material properties and were analyzed using fracture mechanics-based modeling. The results showed that cement line density and osteonal volume had a significant effect on crack volume. The removal of cement lines substantially increased the crack volume in the osteons and interstitial bone, representing straight crack growth, compared to models with cement lines due to the lack of crack deflection in the models without cement lines. Crack volume in the osteons and interstitial bone increased when mean elastic modulus and ultimate strength increased and mean fracture toughness decreased. Crack volume in the osteons and interstitial bone was reduced when material property heterogeneity was incorporated in the models. Although both the microstructure and the heterogeneity of the material properties of the cortical bone independently increased the fracture toughness, the relative contribution of the microstructure was more significant. The integrated experimental-computational framework developed here can identify the most critical microscale features of cortical bone modulated by pathological processes or pharmacological treatments that drive changes in fracture resistance and improve our understanding of the relative influence of microstructure and material properties on fracture resistance of cortical bone.

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models. Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw. The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R² ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models. This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

3D printed trabeculae conditionally reproduce the mechanical properties of the actual trabeculae - A preliminary study

Three-dimensional (3D) printing has been used to fabricate synthetic trabeculae models and to test mechanical behavior that cannot be recognized in the actual sample, but the extent to which 3D printed trabeculae replicate the mechanical behavior of the actual trabeculae remains to be quantified. The aim of this study was to evaluate the accuracy of 3D printed trabeculae in reproducing the mechanical properties of the corresponding actual trabeculae. Twelve human trabecular cubes (5 × 5 × 5 mm) were scanned by micro-CT to form the trabecular 3D model. Each trabecular 3D model was scaled ×2-, ×3-, ×4- and ×5-fold and then printed twice at a layer thickness of 60 μm using poly (lactic acid) (PLA). The actual trabecular cubes and the 3D-printed trabecular cubes were first compressed under a loading rate of 1 mm/min; another replicated stack of 3D-printed trabecular cubes was compressed under a strain rate of 0.2/min. The results showed that the stiffness of the printed cubes tended to increase, while the strength tended to converge when the magnification increased under the two loading conditions. The strain rate effect was found in the printed cubes. The correlation coefficient (R2) of the mechanical properties between the printed and actual trabeculae can reach up to 0.94, especially under ×3-, ×4- and ×5-fold magnification. In conclusion, 3D printing could be a potential tool to evaluate the mechanical behavior of actual trabecular tissue in vitro and may help in the future to predict the risk of fracture and even personalize the treatment evaluation for osteoporosis and other trabecular bone pathologies.

Investigation on the Differences in the Failure Processes of the Cortical Bone under Different Loading Conditions

Cortical bone is a transversely isotropic material, and the mechanical properties may be related to the loading direction on the osteon. Therefore, analyzing the differences in the failure processes of cortical bone under different loading conditions is necessary to explore the measures for reducing the incidence of fracture. In this study, to investigate the effects of different loading directions on the fracture performance in the cortical bone, a numerical method that could simultaneously simulate the failure processes in the cortical bone structure under compression and bending loads was established based on continuum damage mechanics theory. The prediction accuracy and feasibility of the numerical method were first verified by comparing with the corresponding experimental results. Then, the differences in the failure process and fracture performance of the same cortical bone structure under compression and bending loads were investigated. The simulation results indicated that for the same structure, the slip-open failure mode appeared under compression load, and the crack propagated along a certain angle to the loading direction; the tension-open failure mode appeared under bending load, and the crack propagated along the direction perpendicular to the loading direction. Meanwhile, the fracture load was greater and the fracture time was later in the compression than in the bending condition. These phenomena stated that discrepant failure processes and fracture patterns occurred in the same cortical bone structure under different loading conditions. The main reason may be related to the tension–compression asymmetry and transversely isotropic characteristics in the cortical bone material. The fracture simulations in the cortical bone under different loading conditions could improve the prediction accuracy in bone biomechanics and provide the prevention method for cortical bone damage and fracture.

An in silico model for woven bone adaptation to heavy loading conditions in murine tibia

Existing in silico models for lamellar bone adaptation to mechanical loading are unsuitable for predicting woven bone growth. This anomaly is due to the difference in mechanobiology of the woven bone with respect to that of the lamellar bone. The present study is aimed at developing an in silico bone-adaptation model for woven bone at cellular and tissue levels. The diffusion of Ca²⁺ ions reaching lining cells from the osteocytic network and the bone cortex in response to a mechanical loading on the cortical bone has been considered as a stimulus. The diffusion of ions within osteocytic network has been computed with a lacunar-canalicular network (LCN) in which bone cells are uniformly arranged. Strain energy density is assumed to regulate ion flow within the network when the induced normal strain is above a threshold level. If the induced strain exceeds another higher threshold level, then the strain with a power constant is additionally assumed to regulate the stimulus. The intracellular flow of Ca²⁺ ions within the LCN has been simulated using Fick's laws of diffusion, using a finite element method. The ion diffusion from bone cortex to vesicles has been formulated as a normal strain with a power constant. The stimuli reaching the surface cells are assumed to form the new bone. The mathematical model closely predicts woven bone growth in mouse and rat tibia for various in vivo loading conditions. This model is the first to predict woven bone growth at tissue and cellular levels in response to heavy mechanical loading.

Numerical modelling of cancellous bone damage using an orthotropic failure criterion and tissue elastic properties as a function of the mineral content and microporosity

BACKGROUND AND OBJECTIVE

Elastic and strength properties of lamellar tissue are essential to analyze the mechanical behaviour of bone at the meso- or macro-scale. Although many efforts have been made to model the architecture of cancellous bone, in general, isotropic elastic constants are assumed for tissue modelling, neglecting its non-isotropic behaviour. Therefore, isotropic damage laws are often used to estimate the bone failure. The main goals of this work are: (1) to present a new model for the estimation of the elastic properties of lamellar tissue which includes the bone mineral density (BMD) and the microporosity, (2) to address the numerical modelling of cancellous bone damage using an orthotropic failure criterion and a discrete damage mechanics analysis, including the novel approach for the tissue elastic properties aforementioned.

METHODS

Numerical homogenization has been used to estimate the elastic properties of lamellar bone considering BMD and microporosity. Microcomputed Tomography (μ-CT) scans have been performed to obtain the micro-finite element (μ-FE) model of cancellous bone from a vertebra of swine. In this model, lamellar tissue is orientated by considering a unidirectional layer pattern being the mineralized collagen fibrils aligned with the most representative geometrical feature of the trabeculae network. We have considered the Hashin's failure criterion and the Material Property Degradation (MPDG) method for simulating the onset and evolution of bone damage.

RESULTS

The terms of the stiffness matrix for lamellar tissue are derived as functions of the BMD and microporosity at tissue scale. Results obtained for the apparent yield strain values agree with experimental values found in the literature. The influence of the damage parameters on the bone mechanics behaviour is also presented.

CONCLUSIONS

Stiffness matrix of lamellar tissue depends on both BMD and microporosity. The new approach presented in this work enables to analyze the influence of the BMD and porosity on the mechanical response of bone. Lamellar tissue orientation has to be considered in the mechanical analysis of the cancellous bone. An orthotropic failure criterion can be used to analyze the bone failure onset instead of isotropic criteria. The elastic property degradation method is an efficient procedure to analyze the failure propagation in a 3D numerical model.

Numerical Simulation Study of Brittle Rock Materials from Micro to Macro Scales Using Digital Image Processing and Parallel Computing

The multi-scale, high-resolution and accurate structural modeling of rocks is a powerful means to reveal the complex failure mechanisms of rocks and evaluate rock engineering safety. Due to the non-uniformity and opacity of rocks, describing their internal microstructure, mesostructure and macro joints accurately, and how to model their progressive fracture process, is a significant challenge. This paper aims to build a numerical method that can take into account real spatial structures of rocks and be applied to the study of crack propagation and failure in different scales of rocks. By combining the failure process analysis (RFPA) simulator with digital image processing technology, large-scale finite element models of multi-scale rocks, considering microstructure, mesostructure, and macro joints, were created to study mechanical and fracture behaviors on a cloud computing platform. The Windows-Linux interactive method was used for digital image processing and parallel computing. The simulation results show that the combination of a parallel RFPA solver and digital image modeling technology can achieve high-resolution structural modeling and high-efficiency calculation. In microscopic simulations, the influence of shale fractures and mineral spatial distribution on the fracture formation process can be revealed. In the mesostructure simulation, it can be seen that the spatial distribution of minerals has an impact on the splitting mode of the Brazilian splitting model. In the simulation of a joined rock mass, the progressive failure process can be effectively simulated. According to the results, it seems that the finite element parallel computing simulation method based on digital images can simulate the multi-scale failure process of brittle materials from micro to macro scales. Primarily, efficient parallel computing based on a cloud platform allows for the multi-scale, high-resolution and realistic modeling and analysis of rock materials.

Retrospective Evaluation and Framework Development of Bone Anisotropic Material Behavior Compared with Elastic, Elastic-Plastic, and Hyper-Elastic Properties

The main motivation for studying damage in bone tissue is to better understand how damage develops in the bone tissue and how it progresses. Such knowledge may help in the surgical aspects of joint replacement, fracture fixation or establishing the fracture tolerance of bones to prevent injury. Currently, there are no standards that create a realistic bone model with anisotropic material properties, although several protocols have been suggested. This study seeks to retrospectively evaluate the damage of bone tissue with respect to patient demography including age, gender, race, body mass index (BMI), height, and weight, and their role in causing fracture. Investigators believe that properties derived from CT imaging data to estimate the material properties of bone tissue provides more realistic models. Quantifying and associating damage with in vivo conditions will provide the required information to develop mathematical equations and procedures to predict the premature failure and potentially mitigate problems before they begin. Creating a realistic model for bone tissue can predict the premature failure(s), provide preliminary results before getting the surgery, and optimize the design of orthopaedic implants. A comparison was performed between the proposed model and previous efforts, where they used elastic, hyper- elastic, or elastic-plastic properties. Results showed that there was a significant difference between the anisotropic material properties of bone when compared with unrealistic previous methods. The results showed that the density is 50% higher in male subjects than female subjects. Additionally, the results showed that the density is 47.91% higher in Black subjects than Mixed subjects, 53.27% higher than Caucasian subjects and 57.41% higher than Asian. In general, race should be considered during modeling implants or suggesting therapeutic techniques.

Can DXA image-based deep learning model predict the anisotropic elastic behavior of trabecular bone?

3D image-based finite element (FE) and bone volume fraction (BV/TV)/fabric tensor modeling techniques are currently used to determine the apparent stiffness tensor of trabecular bone for assessing its anisotropic elastic behavior. Inspired by the recent success of deep learning (DL) techniques, we hypothesized that DL modeling techniques could be used to predict the apparent stiffness tensor of trabecular bone directly using dual-energy X-ray absorptiometry (DXA) images. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the apparent stiffness tensor of trabecular bone cubes using their DXA images. Trabecular bone cubes obtained from human cadaver proximal femurs were used to obtain simulated DXA images as input, and the apparent stiffness tensor of the trabecular cubes determined by using micro-CT based FE simulations was used as output (ground truth) to train the DL model. The prediction accuracy of the DL model was evaluated by comparing it with the micro-CT based FE models, histomorphometric parameter based multiple linear regression models, and BV/TV/fabric tensor based multiple linear regression models. The results showed that DXA image-based DL model achieved high fidelity in predicting the apparent stiffness tensor of trabecular bone cubes (R² = 0.905-0.973), comparable to or better than the histomorphometric parameter based multiple linear regression and BV/TV/fabric tensor based multiple linear regression models, thus supporting the hypothesis of this study. The outcome of this study could be used to help develop DXA image-based DL techniques for clinical assessment of bone fracture risk.

2D and 3D numerical models to evaluate trabecular bone damage

The comprehension of trabecular bone damage processes could be a crucial hint for understanding how bone damage starts and propagates. Currently, different approaches to bone damage identification could be followed. Clinical approaches start from dual X-ray absorptiometry (DXA) technique that can evaluate bone mineral density (BMD), an indirect indicator of fracture risk. DXA is, in fact, a two-dimensional technology, and BMD alone is not able to predict the effective risk of fractures. First attempts in overcoming this issue have been performed with finite element (FE) methods, combined with the use of three-dimensional high-resolution micro-computed tomographic images. The purpose of this work is to evaluate damage initiation and propagation in trabecular vertebral porcine samples using 2D linear-elastic FE models from DXA images and 3D linear FE models from micro-CT images. Results show that computed values of strains with 2D and 3D approaches (e.g., the minimum principal strain) are of the same order of magnitude. 2D DXA-based models still remain a powerful tool for a preliminary screening of trabecular regions that are prone to fracture, while from 3D micro-CT-based models, it is possible to reach details that permit the localization of the most strained trabecula.

Loss of longitudinal superiority marks the microarchitecture deterioration of osteoporotic cancellous bones

Osteoporosis (OP), a skeletal disease making bone mechanically deteriorate and easily fracture, is a global public health issue due to its high prevalence. It has been well recognized that besides bone loss, microarchitecture degradation plays a crucial role in the mechanical deterioration of OP bones, but the specific role of microarchitecture in OP has not been well clarified and quantified from mechanics perspective. Here, we successfully decoupled and identified the specific roles of microarchitecture, bone mass and tissue property in the failure properties of cancellous bones, through μCT-based digital modeling and finite element method simulations on bone samples from healthy and ovariectomy-induced osteoporotic mice. The results show that the microarchitecture of healthy bones exhibits longitudinal superiority in mechanical properties such as the effective stiffness, strength and toughness, which fits them well to bearing loads along their longitudinal direction. OP does not only reduce bone mass but also impair the microarchitecture topology. The former is mainly responsible for the mechanical degradation of bones in magnitude, wherever the latter accounts for the breakdown of their function-favorable anisotropy, the longitudinal superiority. Hence, we identified the microarchitecture-deterioration-induced directional mismatch between material and loading as a hazardous feature of OP and defined a longitudinal superiority index as measurement of the health status of bone microarchitecture. These findings provide useful insights and guidelines for OP diagnosis and treat assessment.

On challenges in clinical assessment of hip fracture risk using image-based biomechanical modelling: a critical review

INTRODUCTION

Hip fracture is a common health risk among elderly people, due to the prevalence of osteoporosis and accidental fall in the population. Accurate assessment of fracture risk is a crucial step for clinicians to consider patient-by-patient optimal treatments for effective prevention of fractures. Image-based biomechanical modeling has shown promising progress in assessment of fracture risk, and there is still a great possibility for improvement. The purpose of this paper is to identify key issues that need be addressed to improve image-based biomechanical modeling.

MATERIALS AND METHODS

We critically examined issues in consideration and determination of the four biomechanical variables, i.e., risk of fall, fall-induced impact force, bone geometry and bone material quality, which are essential for prediction of hip fracture risk. We closely inspected: limitations introduced by assumptions that are adopted in existing models; deficiencies in methods for construction of biomechanical models, especially for determination of bone material properties from bone images; problems caused by separate use of the variables in clinical study of hip fracture risk; availability of clinical information that are required for validation of biomechanical models.

RESULTS AND CONCLUSIONS

A number of critical issues and gaps were identified. Strategies for effectively addressing the issues were discussed.

Combined Effects of Exercise and Denosumab Treatment on Local Failure in Post-menopausal Osteoporosis-Insights from Bone Remodelling Simulations Accounting for Mineralisation and Damage

Denosumab has been shown to increase bone mineral density (BMD) and reduce the fracture risk in patients with post-menopausal osteoporosis (PMO). Increase in BMD is linked with an increase in bone matrix mineralisation due to suppression of bone remodelling. However, denosumab anti-resorptive action also leads to an increase in fatigue microdamage, which may ultimately lead to an increased fracture risk. A novel mechanobiological model of bone remodelling was developed to investigate how these counter-acting mechanisms are affected both by exercise and long-term denosumab treatment. This model incorporates Frost's mechanostat feedback, a bone mineralisation algorithm and an evolution law for microdamage accumulation. Mechanical disuse and microdamage were assumed to stimulate RANKL production, which modulates activation frequency of basic multicellular units in bone remodelling. This mechanical feedback mechanism controls removal of excess bone mass and microdamage. Furthermore, a novel measure of bone local failure due to instantaneous overloading was developed. Numerical simulations indicate that trabecular bone volume fraction and bone matrix damage are determined by the respective bone turnover and homeostatic loading conditions. PMO patients treated with the currently WHO-approved dose of denosumab (60 mg administrated every 6 months) exhibit increased BMD, increased bone ash fraction and damage. In untreated patients, BMD will significantly decrease, as will ash fraction; while damage will increase. The model predicted that, depending on the time elapsed between the onset of PMO and the beginning of treatment, BMD slowly converges to the same steady-state value, while damage is low in patients treated soon after the onset of the disease and high in patients having PMO for a longer period. The simulations show that late treatment PMO patients have a significantly higher risk of local failure compared to patients that are treated soon after the onset of the disease. Furthermore, overloading resulted in an increase of BMD, but also in a faster increase of damage, which may consequently promote the risk of fracture, specially in late treatment scenarios. In case of mechanical disuse, the model predicted reduced BMD gains due to denosumab, while no significant change in damage occurred, thus leading to an increased risk of local failure compared to habitual loading.

Mechanism and microstructure based concept to predict skull fracture using a hybrid-experimental-modeling-computational approach

Cellular and tissue-scale indent/impact thresholds for different mechanisms of functional impairments to the brain would be the preferred method to predict head injuries, but a comprehensive understanding of the dominant possible injury mechanisms under multiaxial stress-states and rates is currently not available. Until then, skull fracture could serve as an indication of head injury. Therefore the ability to predict the initiation of skull fracture through finite element simulation can serve as an in silico tool for assessing the effectiveness of various head protection scenarios. For this objective, skull fracture initiation was represented with a microstructurally-inspired, mechanism-based (MIMB) failure surface assuming three different dominant mechanisms of skull failure: each element, with deformation and failure properties selected based on its microstructure, was allowed to fail either in tension, compression, or shear, corresponding to clinical linear, depressed or penetrating shear-plug failure (fracture), respectively. Microstructure-inspired a priori values for the initiation threshold of each mechanism, obtained previously from uniaxial and simple-shear experiments, were iterated and optimized for the predicted load-displacement to represent that of the corresponding indentation experiment. Element-level failure enabled the visualization of the evolution of fracture by different mechanisms. The final crack pattern at the time of macroscopic (clinically-identifiable) injury was compared between the simulation and experiment obtained through 3D tomography. Even though the timing was slightly different, the simulated prediction represented remarkably well the experimental crack pattern before the appearance of the catastrophic unstable fast crack in the experiment, thus validating the implemented hybrid-experimental-modeling-computational (HEMC) concept as a tool to predict skull fracture initiation.

Prediction of mechanical properties of trabecular bone in patients with type 2 diabetes using damage based finite element method

Type-2 diabetic (T2D) and osteoporosis (OP) suffered patients are more prone to fragile fracture though the nature of alteration in areal bone mineral density (aBMD) in these two cases are completely different. Therefore, it becomes crucial to compare the effect of T2D and OP on alteration in mechanical and structural properties of femoral trabecular bone. This study investigated the effect of T2D, OP, and osteopenia on bone structural and mechanical properties using micro-CT, nanoindentation and compression test. Further, a nanoscale finite element model (FEM) was developed to predict the cause of alteration in mechanical properties. Finally, a damage-based FEM was proposed to predict the pathological related alteration of bone's mechanical response. The obtained results demonstrated that the T2D group had lower volume fraction (-18.25%, p = 0.023), young's modulus (-23.47%, p = 0.124), apparent modulus (-37.15%, p = 0.02), and toughness (-40%, p = 0.001) than the osteoporosis group. The damage-based FE results were found in good agreement with the compression experiment results for all three pathological conditions. Also, nanoscale FEM results demonstrated that the elastic and failure properties of mineralised collagen fibril decreases with increase in crystal size. This study reveals that T2D patients are more prone to fragile fracture in comparison to OP and osteopenia patients. Also, the proposed damage-based FEM can help to predict the risk of fragility fracture for different pathological conditions.

Investigation of Mechanical, Material, and Compositional Determinants of Human Trabecular Bone Quality in Type 2 Diabetes

CONTEXT

Increased bone fragility and reduced energy absorption to fracture associated with type 2 diabetes (T2D) cannot be explained by bone mineral density alone. This study, for the first time, reports on alterations in bone tissue's material properties obtained from individuals with diabetes and known fragility fracture status.

OBJECTIVE

To investigate the role of T2D in altering biomechanical, microstructural, and compositional properties of bone in individuals with fragility fracture.

METHODS

Femoral head bone tissue specimens were collected from patients who underwent replacement surgery for fragility hip fracture. Trabecular bone quality parameters were compared in samples of 2 groups, nondiabetic (n = 40) and diabetic (n = 30), with a mean duration of disease 7.5 ± 2.8 years.

RESULTS

No significant difference was observed in aBMD between the groups. Bone volume fraction (BV/TV) was lower in the diabetic group due to fewer and thinner trabeculae. The apparent-level toughness and postyield energy were lower in those with diabetes. Tissue-level (nanoindentation) modulus and hardness were lower in this group. Compositional differences in the diabetic group included lower mineral:matrix, wider mineral crystals, and bone collagen modifications-higher total fluorescent advanced glycation end-products (fAGEs), higher nonenzymatic cross-link ratio (NE-xLR), and altered secondary structure (amide bands). There was a strong inverse correlation between NE-xLR and postyield strain, fAGEs and postyield energy, and fAGEs and toughness.

CONCLUSION

The current study is novel in examining bone tissue in T2D following first hip fragility fracture. Our findings provide evidence of hyperglycemia's detrimental effects on trabecular bone quality at multiple scales leading to lower energy absorption and toughness indicative of increased propensity to bone fragility.

Open cell polyurethane foam compression failure characterization and its relationship to morphometry

Open cell polyurethane foams are often used as cancellous bone surrogates because of their similarities in morphology and mechanical response. In this work, open cell polyurethane foams of three different densities are characterized from morphometric and mechanical perspectives. The analysis of micro-computed tomography images has revealed that the high density foams present the greatest inhomogeneities. Those inhomogeneities promoted the failure location. We have used the finite element models as a tool to estimate elastic and failure properties that can be used in numerical modeling. Furthermore, we have assessed the anisotropic mechanical response of the foams, whose differences are related to the morphometric inhomogeneities. We found significant relationships between morphometry and the elastic and failure response. The detailed information about morphometry, elastic constants and strength limits provided in this work can be of interest to researchers and practitioners that often use these polyurethane foams in orthopedic implants and cement augmentation evaluations.

Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σ_f) for each element were modeled by BVF (f_BV) power functional relationships of the form: [Formula: see text] MPa. The initial leading coefficients (σ_f,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.

A Review on Recent Advances in the Constitutive Modeling of Bone Tissue

PURPOSE OF REVIEW

Image-based finite element analysis (FEA) to predict and understand the biomechanical response has become an essential methodology in musculoskeletal research. An important part of such simulation models is the constitutive material model of which recent advances are summarized in this review.

RECENT FINDINGS

The review shows that existing models from other fields were introduced, such as cohesion zone (cortical bone) or phase-field models (trabecular bone). Some progress has been made in describing cortical bone involving physical mechanisms such as microcracks. Problems with validations at different length scales remain a problem. The improvement of recent constitutive models is partially obscured by uncertainties that affect overall predictions, such as image quality and calibration or boundary conditions. Nevertheless, in vivo CT-based FEA simulations based on a sophisticated constitutive behavior are a very valuable tool for clinical-related osteoporosis research.

Validation of HR-pQCT against micro-CT for morphometric and biomechanical analyses: A review

High-resolution peripheral quantitative computed-tomography (HR-pQCT) has the potential to become a powerful clinical assessment and diagnostic tool. Given the recent improvements in image resolution, from 82 to 61 μm, this technology may be used to accurately quantify in vivo bone microarchitecture, a key biomarker of degenerative bone diseases. However, computational methods to assess bone microarchitecture were developed for micro computed tomography (micro-CT), a higher-resolution technology only available for ex vivo studies, and validation of these computational analysis techniques against the gold-standard micro-CT has been inconsistent and incomplete. Herein, we review methods for segmentation of bone compartments and microstructure, quantification of bone morphology, and estimation of mechanical strength using finite-element analysis, highlighting the need throughout for improved standardization across the field. Studies have relied on homogenous datasets for validation, which does not allow for robust comparisons between methods. Consequently, the adaptation and validation of novel segmentation approaches has been slow to non-existent, with most studies still using the manufacturer's segmentation for morphometric analysis despite the existence of better performing alternative approaches. The promising accuracy of HR-pQCT for capturing morphometric indices is overshadowed by considerable variability in outcomes between studies. For finite element analysis (FEA) methods, the use of disparate material models and FEA tools has led to a fragmented ability to assess mechanical bone strength with HR-pQCT. Further, the scarcity of studies comparing 62 μm HR-pQCT to the gold standard micro-CT leaves the validation of this imaging modality incomplete. This review revealed that without standardization, the capabilities of HR-pQCT cannot be adequately assessed. The need for a public, extendable, heterogeneous dataset of HR-pQCT and corresponding gold-standard micro-CT images, which would allow HR-pQCT users to benchmark existing and novel methods and select optimal methods depending on the scientific question and data at hand, is now evident. With more recent advancements in HR-pQCT, the community must learn from its past and provide properly validated technologies to ensure that HR-pQCT can truly provide value in patient diagnosis and care.

Differences in the microarchitectural features of the lateral collapsed lesion between osteonecrosis and subchondral insufficiency fracture of the femoral head

BACKGROUND

Like osteonecrosis of the femoral head (ONFH), subchondral insufficiency fracture of the femoral head (SIF) causes femoral head collapse. However, little is known about the differences between the two diseases regarding the morphological features of the collapsed lesion. We tested the hypothesis that the morphological features of the lateral collapsed lesion would differ between ONFH and SIF.

METHODS

Twenty femoral heads histopathologically diagnosed as ONFH (n = 10) or SIF (n = 10) were used in this study. In the lateral collapsed lesion of each femoral head, cubic regions of interest (ROIs) were selected within the collapsed subchondral area and the nearby non-collapsed subchondral area. Micro-CT-based microarchitectural parameters were compared between the ROIs in each disease. Additionally, correlations between histopathological and microarchitectural features were evaluated.

RESULTS

In ONFH, bone volume fraction, trabecular thickness, and bone mineral density in the collapsed area were all significantly lower than those in the nearby non-collapsed area where thickened bone trabeculae accompanied by appositional bone formation were invariably seen. On the other hand, in SIF there were no significant differences between the ROIs in any of these microarchitectural parameters. Histopathologically, varying degrees of callus formation overlying the fracture of the subchondral plate were seen around the lateral collapsed lesion.

CONCLUSION

The morphological features of the lateral collapsed lesion were inconsistent between ONFH and SIF, suggesting different pathomechanisms of femoral head collapse.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Early tibial subchondral bone texture changes after arthroscopic partial meniscectomy in knees without radiographic OA: A prospective cohort study

Arthroscopic partial meniscectomy (APM) may lead to changes in underlying trabecular bone (TB) structure potentially promoting the development of knee joint osteoarthritis. Our aim was to investigate if there are early changes occurring in tibial subchondral TB texture in the leg undergoing medial APM compared with the unoperated non-injured contra-lateral leg. The bone texture was measured as the medial-to-lateral ratio of fractal dimensions (FD) calculated for regions selected on weight-bearing anteroposterior tibiofemoral x-rays. Twenty-one subjects before and 12 months after APM were included from 374 patients scheduled for unilateral medial APM. The medial-to-lateral ratio was calculated for horizontal, vertical, and roughest FDs respectively. Higher FD means higher bone roughness. Each FD was calculated over a range of scales using a variance orientation transform method. Mean values of medial-to-lateral horizontal FD calculated for APM knees at follow-up were higher than those at baseline. For unoperated knees the values were lower. The difference in the horizontal FD change from baseline to follow-up between APM and contra-lateral legs was 0.028 (95% CI, 0.004-0.052). The bone roughness changes may reflect the increase in peak knee adduction moment (KAM) and KAM impulse during walking reported for the same cohort in a previous study. They may also reflect early signs of osteoarthritis development and thus, we speculate that individuals with increased bone texture roughness ratio after APM might be at higher risk of knee osteoarthritis development.

Prediction of failure in cancellous bone using extended finite element method

The objective of our study is to develop extended finite element method models of cancellous bone specimens that are capable of accurately predicting the onset and propagation of cracks under mechanical loading. In order to do so, previously published three-point bending test results of a single trabecula were replicated using two different extended finite element method approaches, namely, elastic-plastic-fracture and elastic-fracture that considered different configurations of the elasto-plastic properties of bone from which the best approach to fit the experimental data was identified. The behavior of a single trabecula was then used in 2D extended finite element method models to quantify the strength of the trabecular tissue of the forearm along three perpendicular anatomical axes. The results revealed that the elastic-plastic-fracture model better represented the experimental data in the model of a single trabecula. Considering the 2D trabecular specimens, the elastic fracture model predicted higher strength than the elastic-plastic-fracture model and there was no difference in stiffness between the two models. In general, the specimens exhibited higher failure strain and more ductile behavior in compression than in tension. In addition, strength and stiffness were found to be higher in tension than compression on average. It can be concluded that with proper parameters, extended finite element method is capable of simulating the ductile behavior of cancellous bone. The models are able to quantify the tensile strength of trabecular tissue in the various anatomical directions reporting an increased strength in the longitudinal direction of forearm cancellous bone tissue. Extended finite element method of cancellous bone proves to be a valuable tool to predict the mechanical characteristics of cancellous bones as a function of the microstructure.

Multiscale design of artificial bones with biomimetic elastic microstructures

Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

A new finite element based parameter to predict bone fracture

Dual Energy X-Ray Absorptiometry (DXA) is currently the most widely adopted non-invasive clinical technique to assess bone mineral density and bone mineral content in human research and represents the primary tool for the diagnosis of osteoporosis. DXA measures areal bone mineral density, BMD, which does not account for the three-dimensional structure of the vertebrae and for the distribution of bone mass. The result is that longitudinal DXA can only predict about 70% of vertebral fractures. This study proposes a complementary tool, based on Finite Element (FE) models, to improve the DXA accuracy. Bone is simulated as elastic and inhomogeneous material, with stiffness distribution derived from DXA greyscale images of density. The numerical procedure simulates a compressive load on each vertebra to evaluate the local minimum principal strain values. From these values, both the local average and the maximum strains are computed over the cross sections and along the height of the analysed bone region, to provide a parameter, named Strain Index of Bone (SIB), which could be considered as a bone fragility index. The procedure is initially validated on 33 cylindrical trabecular bone samples obtained from porcine lumbar vertebrae, experimentally tested under static compressive loading. Comparing the experimental mechanical parameters with the SIB, we could find a higher correlation of the ultimate stress, σULT, with the SIB values (R2adj = 0.63) than that observed with the conventional DXA-based clinical parameters, i.e. Bone Mineral Density, BMD (R2adj = 0.34) and Trabecular Bone Score, TBS (R2adj = -0.03). The paper finally presents a few case studies of numerical simulations carried out on human lumbar vertebrae. If our results are confirmed in prospective studies, SIB could be used-together with BMD and TBS-to improve the fracture risk assessment and support the clinical decision to assume specific drugs for metabolic bone diseases.

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

An efficient solver for large-scale linear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \hbox {FE}$$\end{document}μFE 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${36}\,{{\upmu }\hbox {m}}$$\end{document}36μm. 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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2 > 0.97$$\end{document}R2>0.97). 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.

A novel phase field method for modeling the fracture of long bones

A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power-law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

Microstructure-based numerical computational method for the insertion torque of dental implant

The bone quality has a significant effect on the insertion torque of dental implant. In most clinical studies, bone density is used as a gold standard in predicting insertion torque. By contrast, trabecular microstructure is ignored. In this study, a microstructure-based numerical computational method with high accuracy and efficiency for the insertion torque of dental implant was proposed by introducing two microscopic variables, namely, volume fraction and fabric tensor. First, two kinds of 3D microstructural solid models with same volume fraction and fabric tensor were established on the basis of the microstructural topology of six reference specimens. Second, a new numerical simulation method based on homogenous theory was used to explore the material models of these 3D microstructural solid models at the microscopic scale. Then, the anisotropic material models of specimens were developed on the basis of the mixture rule. Thereafter, a numerical simulation based on the anisotropic finite element (FE) model was carried out to acquire the insertion torque. To demonstrate the efficiency and accuracy of the simulation based on the anisotropic FE model, numerical simulations based on isotropic FE model and micro-computer tomography (micro-CT) FE models were also implemented as comparisons. Comparison of the simulated peak insertion torques of the anisotropic, isotropic, and micro-CT FE models with insertion experiments demonstrated the feasibility and potential of the proposed method. The anisotropic FE model reduced the time consumption by 91.85% and enhanced the accuracy by 11.82% compared with the micro-CT and isotropic FE models, respectively.

On dynamic behavior of bone: Experimental and numerical study of porcine ribs subjected to impact loads in dynamic three-point bending tests

This study covers the characterization of the dynamic behavior of isolated porcine ribs based on experimental and numerical approaches. A Split Hopkinson Pressure Bar (SHPB) setup for three-point bending tests was used. Data of 20 tests were considered to be comprehensible for experimental characterization, thereby, showing an influence of strain rate on both time for fracture and amplitudes of force response. A three-dimensional porcine rib model was generated from the DICOM (Digital Imaging and Communication in Medicine) images of High-Resolution peripheral Quantitative Computed Tomography (HR-pQCT) scans. Material properties having been fitted by power law regression equations based on apparent density were assigned to the numerical rib. A modified elastic-plastic constitutive law, capable of considering the effects of strain rate was adopted. An incremental and stress-state dependent damage law, capable of considering effects of strain rate on fracture propagation, non-linear damage accumulation and instabilities was coupled to the constitutive law. The Finite Element (FE) model shows high efficiency in predicting both force-displacement curve and the fracture patterns of tested ribs. Predictions prove the ability of the proposed model to investigate the fracture behavior of human ribs under dynamic loads.

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.

Current state of fabrication technologies and materials for bone tissue engineering

A range of traditional and free-form fabrication technologies have been investigated and, in numerous occasions, commercialized for use in the field of regenerative tissue engineering (TE). The demand for technologies capable of treating bone defects inherently difficult to repair has been on the rise. This quest, accompanied by the advent of functionally tailored, biocompatible, and biodegradable materials, has garnered an enormous research interest in bone TE. As a result, different materials and fabrication methods have been investigated towards this end, leading to a deeper understanding of the geometrical, mechanical and biological requirements associated with bone scaffolds. As our understanding of the scaffold requirements expands, so do the capability requirements of the fabrication processes. The goal of this review is to provide a broad examination of existing scaffold fabrication processes and highlight future trends in their development. To appreciate the clinical requirements of bone scaffolds, a brief review of the biological process by which bone regenerates itself is presented first. This is followed by a summary and comparisons of commonly used implant techniques to highlight the advantages of TE-based approaches over traditional grafting methods. A detailed discussion on the clinical and mechanical requirements of bone scaffolds then follows. The remainder of the manuscript is dedicated to current scaffold fabrication methods, their unique capabilities and perceived shortcomings. The range of biomaterials employed in each fabrication method is summarized. Selected traditional and non-traditional fabrication methods are discussed with a highlight on their future potential from the authors' perspective. This study is motivated by the rapidly growing demand for effective scaffold fabrication processes capable of economically producing constructs with intricate and precisely controlled internal and external architectures. STATEMENT OF SIGNIFICANCE: The manuscript summarizes the current state of fabrication technologies and materials used for creating scaffolds in bone tissue engineering applications. A comprehensive analysis of different fabrication methods (traditional and free-form) were summarized in this review paper, with emphasis on recent developments in the field. The fabrication techniques suitable for creating scaffolds for tissue engineering was particularly targeted and their use in bone tissue engineering were articulated. Along with the fabrication techniques, we emphasized the choice of materials in these processes. Considering the limitations of each process, we highlighted the materials and the material properties critical in that particular process and provided a brief rational for the choice of the materials. The functional performance for bone tissue engineering are summarized for different fabrication processes and the choice of biomaterials. Finally, we provide a perspective on the future of the field, highlighting the knowledge gaps and promising avenues in pursuit of effective scaffolds for bone tissue engineering. This extensive review of the field will provide research community with a reference source for current approaches to scaffold preparation. We hope to encourage the researchers to generate next generation biomaterials to be used in these fabrication processes. By providing both advantages and disadvantage of each fabrication method in detail, new fabrication techniques might be devised that will overcome the limitations of the current approaches. These studies should facilitate the efforts of researchers interested in generating ideal scaffolds, and should have applications beyond the repair of bone tissue.

Determinants of bone damage: An ex-vivo study on porcine vertebrae

Bone's resistance to fracture depends on several factors, such as bone mass, microarchitecture, and tissue material properties. The clinical assessment of bone strength is generally performed by Dual-X Ray Photon Absorptiometry (DXA), measuring bone mineral density (BMD) and trabecular bone score (TBS). Although it is considered the major predictor of bone strength, BMD only accounts for about 70% of fragility fractures, while the remaining 30% could be described by bone "quality" impairment parameters, mainly related to tissue microarchitecture. The assessment of bone microarchitecture generally requires more invasive techniques, which are not applicable in routine clinical practice, or X-Ray based imaging techniques, requiring a longer post-processing. Another important aspect is the presence of local damage in the bony tissue that may also affect the prediction of bone strength and fracture risk. To provide a more comprehensive analysis of bone quality and quantity, and to assess the effect of damage, here we adopt a framework that includes clinical, morphological, and mechanical analyses, carried out by means of DXA, μCT and mechanical compressive testing, respectively. This study has been carried out on trabecular bones, taken from porcine trabecular vertebrae, for the similarity with human lumbar spine. This study confirms that no single method can provide a complete characterization of bone tissue, and the combination of complementary characterization techniques is required for an accurate and exhaustive description of bone status. BMD and TBS have shown to be complementary parameters to assess bone strength, the former assessing the bone quantity and resistance to damage, and the latter the bone quality and the presence of damage accumulation without being able to predict the risk of fracture.

Exercise Early and Often: Effects of Physical Activity and Exercise on Women's Bone Health

In 2011 over 1.7 million people were hospitalized because of a fragility fracture, and direct costs associated with osteoporosis treatment exceeded 70 billion dollars in the United States. Failure to reach and maintain optimal peak bone mass during adulthood is a critical factor in determining fragility fracture risk later in life. Physical activity is a widely accessible, low cost, and highly modifiable contributor to bone health. Exercise is especially effective during adolescence, a time period when nearly 50% of peak adult bone mass is gained. Here, we review the evidence linking exercise and physical activity to bone health in women. Bone structure and quality will be discussed, especially in the context of clinical diagnosis of osteoporosis. We review the mechanisms governing bone metabolism in the context of physical activity and exercise. Questions such as, when during life is exercise most effective, and what specific types of exercises improve bone health, are addressed. Finally, we discuss some emerging areas of research on this topic, and summarize areas of need and opportunity.

Distal radius microstructure and finite element bone strain are related to site-specific mechanical loading and areal bone mineral density in premenopausal women

While weight-bearing and resistive exercise modestly increases aBMD, the precise relationship between physical activity and bone microstructure, and strain in humans is not known. Previously, we established a voluntary upper-extremity loading model that assigns a person's target force based on their subject-specific, continuum FE-estimated radius bone strain. Here, our purpose was to quantify the inter-individual variability in radius microstructure and FE-estimated strain explained by site-specific mechanical loading history, and to determine whether variability in strain is captured by aBMD, a clinically relevant measure of bone density and fracture risk. Seventy-two women aged 21–40 were included in this cross-sectional analysis. High resolution peripheral quantitative computed tomography (HRpQCT) was used to measure macro- and micro-structure in the distal radius. Mean energy equivalent strain in the distal radius was calculated from continuum finite element models generated from clinical resolution CT images of the forearm. Areal BMD was used in a nonlinear regression model to predict FE strain. Hierarchical linear regression models were used to assess the predictive capability of intrinsic (age, height) and modifiable (body mass, grip strength, physical activity) predictors. Fifty-one percent of the variability in FE bone strain was explained by its relationship with aBMD, with higher density predicting lower strains. Age and height explained up to 31.6% of the variance in microstructural parameters. Body mass explained 9.1% and 10.0% of the variance in aBMD and bone strain, respectively, with higher body mass indicative of greater density. Overall, results suggest that meaningful differences in bone structure and strain can be predicted by subject characteristics.

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Areal bone mineral density (aBMD) explains 51% of the variability in bone strain.

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Adult bone loading predicts greater cortical porosity and trabecular density.

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Greater body mass predicts greater aBMD and lower bone strain.

Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

The potential role of variations in juvenile hip geometry on the development of Legg-Calvé-Perthes disease: a biomechanical investigation

Legg-Calvé-Perthes disease (LCP) is one of the most poorly understood diseases in paediatric orthopaedics. One common trait of LCP is the marked morphological difference between healthy and pathological hips, early deviations of which (i.e. prior to disease onset) have been suggested to lead to the overload and collapse of the epiphysis. Here, the impact of common variations in geometry is investigated with a finite element model of a juvenile femur under single leg standing and landing. Here, the impact of typical variations in geometry is investigated with a finite element model of a juvenile femur under single leg standing and landing. The variations appear to have only a limited effect on the stress distribution in the femoral epiphysis even during high impact activities. This suggests that, for this individual at least, they would be unlikely to cause epiphyseal overload and collapse, even in the presence of a skeletally immature epiphysis.

Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures

The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then used to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, ie, the interface width of the phase field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body.

Determination of a tissue-level failure evaluation standard for rat femoral cortical bone utilizing a hybrid computational-experimental method

Macro-level failure in bone structure could be diagnosed by pain or physical examination. However, diagnosing tissue-level failure in a timely manner is challenging due to the difficulty in observing the interior mechanical environment of bone tissue. Because most fractures begin with tissue-level failure in bone tissue caused by continually applied loading, people attempt to monitor the tissue-level failure of bone and provide corresponding measures to prevent fracture. Many tissue-level mechanical parameters of bone could be predicted or measured; however, the value of the parameter may vary among different specimens belonging to a kind of bone structure even at the same age and anatomical site. These variations cause difficulty in representing tissue-level bone failure. Therefore, determining an appropriate tissue-level failure evaluation standard is necessary to represent tissue-level bone failure. In this study, the yield and failure processes of rat femoral cortical bones were primarily simulated through a hybrid computational-experimental method. Subsequently, the tissue-level strains and the ratio between tissue-level failure and yield strains in cortical bones were predicted. The results indicated that certain differences existed in tissue-level strains; however, slight variations in the ratio were observed among different cortical bones. Therefore, the ratio between tissue-level failure and yield strains for a kind of bone structure could be determined. This ratio may then be regarded as an appropriate tissue-level failure evaluation standard to represent the mechanical status of bone tissue.

Macrodamage Accumulation Model for a Human Femur

The objective of this study was to more fully understand the mechanical behavior of bone tissue that is important to find an alternative material to be used as an implant and to develop an accurate model to predict the fracture of the bone. Predicting and preventing bone failure is an important area in orthopaedics. In this paper, the macrodamage accumulation models in the bone tissue have been investigated. Phenomenological models for bone damage have been discussed in detail. In addition, 3D finite element model of the femur prepared from imaging data with both cortical and trabecular structures is delineated using MIMICS and ANSYS® and simulated as a composite structure. The damage accumulation occurring during cyclic loading was analyzed for fatigue scenario. We found that the damage accumulates sooner in the multiaxial than in the uniaxial loading condition for the same number of cycles, and the failure starts in the cortical bone. The damage accumulation behavior seems to follow a three-stage growth: a primary phase, a secondary phase of damage growth marked by linear damage growth, and a tertiary phase that leads to failure. Finally, the stiffness of the composite bone comprising the cortical and trabecular bone was significantly different as expected.

Influence of the shape of the micro-finite element model on the mechanical properties calculated from micro-finite element analysis

Assessing the biomechanical properties of trabecular bone is of major biological and clinical significance for the research of bone diseases, fractures and their treatments. Micro-finite element (µFE) models are becoming increasingly popular for investigating the biomechanical properties of trabecular bone. The shapes of µFE models typically include cube and cylinder. Whether there are differences between cubic and cylindrical µFE models has not yet been studied. In the present study, cubic and cylindrical µFE models of human vertebral trabecular bone were constructed. A 1% strain was prescribed to the model along the superior-inferior direction. E values were calculated from these models, and paired t-tests were performed to determine whether these were any differences between E values obtained from cubic and cylindrical models. The results demonstrated that there were no statistically significant differences in the E values between cubic and cylindrical models, and there were no significant differences in Von Mises stress distributions between the two models. These findings indicated that, to construct µFE models of vertebral trabecular bone, cubic or cylindrical models were both feasible. Choosing between the cubic or cylindrical µFE model is dependent upon the specific study design.