Multi-axial mechanical properties of human trabecular bone

Integrated analysis of clinical indicators and mechanical properties in cancellous bone

Cancellous bone plays a critical role as a shock absorber in the human skeletal system. Accurate assessment of its microstructure and mechanical properties is crucial for osteoporosis diagnosis and treatment. However, various methods with different indicators are adopted currently in the clinical and laboratory assessments which lead to confusion and inconvenience for cancellous bone analysis. In the current work, correlations among clinical indicators including CT-derived Hounsfield Unit (HU) & bone mineral density (BMD), laboratory indicators (mass density & volume fraction), and mechanical properties (modulus & strength) are explored. The results show that different indicators can be linearly linked through the HU value which can be adopted as a good microstructure indicator of cancellous bone. Additionally, the impacts of cancellous bone specimen preparation on clinical CT imaging and mechanical properties are also investigated. The results indicate common marrow-removal treatment can lead to decrease in mean HU value, deviation in HU value distribution, while it will increase the modulus and strength. The current work provides a valuable insight into the cancellous properties based on comprehensive analysis on the clinical and laboratory assessments which is critical for accurate diagnosis and personalized treatment.

Mechanical properties of additively manufactured lattice structures composed of zirconia and hydroxyapatite ceramics

Ceramic lattices hold great potential for bone scaffolds to facilitate bone regeneration and integration of native tissue with medical implants. While there have been several studies on additive manufacturing of ceramics and their osseointegrative and osteoconductive properties, there is a lack of a comprehensive examination of their mechanical behavior. Therefore, the aim of this study was to assess the mechanical properties of different additively manufactured ceramic lattice structures under different loading conditions and their overall ability to mimic bone tissue properties. Eleven different lattice structures were designed and manufactured with a porosity of 80% using two materials, hydroxyapatite (HAp) and zirconium dioxide (ZrO2). Six cell-based lattices with cubic and hexagonal base, as well as five Voronoi-based lattices were considered in this study. The samples were manufactured using lithography-based ceramic additive manufacturing and post-processed thermally prior to mechanical testing. Cell-based lattices with cubic and hexagonal base, as well as Voronoi-based lattices were considered in this study. The lattices were tested under four loading conditions: compression, four-point bending, shear and tension. The manufacturing process of the different ceramics leads to different deviations of the lattice geometry, hence, the elastic properties of one structure cannot be directly inferred from one material to another. ZrO2 lattices prove to be stiffer than HAp lattices of the same designed structure. The Young's modulus for compression of ZrO2 lattices ranges from 2 to 30GPa depending on the used lattice design and for HAp 200MPa to 3.8GPa. The expected stability, the load where 63.2% of the samples are expected to be destroyed, of the lattices ranges from 81 to 553MPa and for HAp 6 to 42MPa. For the first time, a comprehensive overview of the mechanical properties of various additively manufactured ceramic lattice structures is provided. This is intended to serve as a reference for designers who would like to expand the design capabilities of ceramic implants that will lead to an advancement in their performance and ability to mimic human bone tissue.

Explainable Ensemble Learning and Multilayer Perceptron Modeling for Compressive Strength Prediction of Ultra-High-Performance Concrete

The performance of ultra-high-performance concrete (UHPC) allows for the design and creation of thinner elements with superior overall durability. The compressive strength of UHPC is a value that can be reached after a certain period of time through a series of tests and cures. However, this value can be estimated by machine-learning methods. In this study, multilayer perceptron (MLP) and Stacking Regressor, an ensemble machine-learning models, is used to predict the compressive strength of high-performance concrete. Then, the ML model's performance is explained with a feature importance analysis and Shapley additive explanations (SHAPs), and the developed models are interpreted. The effect of using different random splits for the training and test sets has been investigated. It was observed that the stacking regressor, which combined the outputs of Extreme Gradient Boosting (XGBoost), Category Boosting (CatBoost), Light Gradient Boosting Machine (LightGBM), and Extra Trees regressors using random forest as the final estimator, performed significantly better than the MLP regressor. It was shown that the compressive strength was predicted by the stacking regressor with an average R2 score of 0.971 on the test set. On the other hand, the average R2 score of the MLP model was 0.909. The results of the SHAP analysis showed that the age of concrete and the amounts of silica fume, fiber, superplasticizer, cement, aggregate, and water have the greatest impact on the model predictions.

Freezing does not influence the microarchitectural parameters of the microstructure of the freshly harvested femoral head bone

The femoral head is one of the most commonly used bones for allografts and biomechanical studies. However, there are few reports on the trabecular bone microarchitectural parameters of freshly harvested trabecular bones. To our knowledge, this is the first study to characterize the microstructure of femoral heads tested immediately after surgery and compare it with the microstructure obtained with conventional freezing. This study aims to investigate whether freezing at -80 °C for 6 weeks affects the trabecular microstructure of freshly harvested bone tissue. This study was divided into two groups: one with freshly harvested human femoral heads and the other with the same human femoral heads frozen at -80 °C for 6 weeks. Each femoral head was scanned using an X-ray microcomputed tomography scanner (µCT) to obtain the microarchitectural parameters, including the bone volume fraction (BV/TV), the mean trabecular thickness (Tb.th), the trabecular separation (Tb.sp), the degree of anisotropy (DA), and the connectivity density (Conn.D). There was no statistically significant difference between the fresh and the frozen groups for any of the parameters measured. This study shows that freezing at -80 °C for 6 weeks does not alter bone microstructure compared with freshly harvested femoral heads tested immediately after surgery.

Comparing ceramic Fischer-Koch-S and gyroid TPMS scaffolds for potential in bone tissue engineering

Triply Periodic Minimal Surfaces (TPMS), such as Gyroid, are widely accepted for bone tissue engineering due to their interconnected porous structures with tunable properties that enable high surface area to volume ratios, energy absorption, and relative strength. Among these topologies, the Fischer-Koch-S (FKS) has also been suggested for compact bone scaffolds, but few studies have investigated these structures beyond computer simulations. FKS scaffolds have been fabricated in metal and polymer, but to date none have been fabricated in a ceramic used in bone tissue engineering (BTE) scaffolds. This study is the first to fabricate ceramic FKS scaffolds and compare them with the more common Gyroid topology. Results showed that FKS scaffolds were 32% stronger, absorbed 49% more energy, and had only 11% lower permeability than Gyroid scaffolds when manufactured at high porosity (70%). Both FKS and Gyroid scaffolds displayed strength and permeability in the low range of trabecular long bones with high reliability (Weibull failure probability) in the normal direction. Fracture modes were further investigated to explicate the quasi-brittle failure exhibited by both scaffold topologies, exploring stress-strain relationships along with scanning electron microscopy for failure analysis. Considering the physical aspects of successful bone tissue engineering scaffolds, FKS scaffolds appear to be more promising for further study as bone regeneration scaffolds than Gyroid due to their higher compressive strength and reliability, at only a small penalty to permeability. In the context of BTE, FKS scaffolds may be better suited than Gyroids to applications where denser bone and strength is prioritized over permeability, as suggested by earlier simulation studies.

Finite element models with automatic computed tomography bone segmentation for failure load computation

Bone segmentation is an important step to perform biomechanical failure load simulations on in-vivo CT data of patients with bone metastasis, as it is a mandatory operation to obtain meshes needed for numerical simulations. Segmentation can be a tedious and time consuming task when done manually, and expert segmentations are subject to intra- and inter-operator variability. Deep learning methods are increasingly employed to automatically carry out image segmentation tasks. These networks usually need to be trained on a large image dataset along with the manual segmentations to maximize generalization to new images, but it is not always possible to have access to a multitude of CT-scans with the associated ground truth. It then becomes necessary to use training techniques to make the best use of the limited available data. In this paper, we propose a dedicated pipeline of preprocessing, deep learning based segmentation method and post-processing for in-vivo human femurs and vertebrae segmentation from CT-scans volumes. We experimented with three U-Net architectures and showed that out-of-the-box models enable automatic and high-quality volume segmentation if carefully trained. We compared the failure load simulation results obtained on femurs and vertebrae using either automatic or manual segmentations and studied the sensitivity of the simulations on small variations of the automatic segmentation. The failure loads obtained using automatic segmentations were comparable to those obtained using manual expert segmentations for all the femurs and vertebrae tested, demonstrating the effectiveness of the automated segmentation approach for failure load simulations.

In vitro evaluation of the osteogenic and antimicrobial potential of porous wollastonite scaffolds impregnated with ethanolic extracts of propolis

Context: The development of porous devices using materials modified with various natural agents has become a priority for bone healing processes in the oral and maxillofacial field. There must be a balance between the proliferation of eukaryotic and the inhibition of prokaryotic cells to achieve proper bone health. Infections might inhibit the formation of new alveolar bone during bone graft augmentation. Objective: This study aimed to evaluate the in vitro osteogenic behavior of human bone marrow stem cells and assess the antimicrobial response to 3D-printed porous scaffolds using propolis-modified wollastonite. Methodology: A fractional factorial design of experiments was used to obtain a 3D printing paste for developing scaffolds with a triply periodic minimal surface (TPMS) gyroid geometry based on wollastonite and modified with an ethanolic propolis extract. The antioxidant activity of the extracts was characterized using free radical scavenging methods (DPPH and ABTS). Cell proliferation and osteogenic potential using Human Bone Marrow Stem Cells (bmMSCs) were assessed at different culture time points up to 28 days. MIC and inhibition zones were studied from single strain cultures, and biofilm formation was evaluated on the scaffolds under co-culture conditions. The mechanical strength of the scaffolds was evaluated. Results: Through statistical design of experiments, a paste suitable for printing scaffolds with the desired geometry was obtained. Propolis extracts modifying the TPMS gyroid scaffolds showed favorable cell proliferation and metabolic activity with osteogenic potential after 21 days. Additionally, propolis exhibited antioxidant activity, which may be related to the antimicrobial effectiveness of the scaffolds against S. aureus and S. epidermidis cultures. The mechanical properties of the scaffolds were not affected by propolis impregnation. Conclusion: These results demonstrate that propolis-impregnated porous wollastonite scaffolds might have the potential to stimulate bone repair in maxillofacial tissue engineering applications.

Antibacterial and osteoinductive properties of wollastonite scaffolds impregnated with propolis produced by additive manufacturing

Biocompatible ceramic scaffolds offer a promising approach to address the challenges in bone reconstruction. Wollastonite, well-known for its exceptional biocompatibility, has attracted significant attention in orthopedics and craniofacial fields. However, the antimicrobial properties of wollastonite have contradictory findings, necessitating further research to enhance its antibacterial characteristics. This study aimed to explore a new approach to improve in vitro biological response in terms of antimicrobial activity and cell proliferation by taking advantage of additive manufacturing for the development of scaffolds with complex geometries by 3D printing using propolis-modified wollastonite. The scaffolds were designed with a TPMS (Triply Periodic Minimal Surface) gyroid geometric shape and 3D printed prior to impregnation with propolis extract. The paste formulation was characterized by rheometric measurements, and the presence of propolis was confirmed by FTIR spectroscopy. The scaffolds were comprehensively assessed for their mechanical strength. The biological characterization involved evaluating the antimicrobial effects against Staphylococcus aureus and Staphylococcus epidermidis, employing Minimum Inhibitory Concentration (MIC), Zone of Inhibition (ZOI), and biofilm formation assays. Additionally, SaOs-2 cultures were used to study cell proliferation (Alamar blue assay), and potential osteogenic was tested (von Kossa, Alizarin Red, and ALP stainings) at different time points. Propolis impregnation did not compromise the mechanical properties of the scaffolds, which exhibited values comparable to human trabecular bone. Propolis incorporation conferred antibacterial activity against both Staphylococcus aureus and Staphylococcus epidermidis. The implementation of TPMS gyroid geometry in the scaffold design demonstrated favorable cell proliferation with increased metabolic activity and osteogenic potential after 21 days of cell cultures.

An improved trabecular bone model based on Voronoi tessellation

BACKGROUND AND OBJECTIVE

Accurate numerical and physical models of trabecular bone, correctly representing its complexity and variability, could be highly advantageous in the development of e.g. new bone-anchored implants due to the limited availability of real bone. Several Voronoi tessellation-based porous models have been reported in the literature, attempting to mimic the trabecular bone. However, these models have been limited to lattice rod-like structures, which are only structurally representative of very high-porosity trabecular bone. The objective of this study was to provide an improved model, more representative of trabecular bone of different porosity.

METHODS

Boolean operations were utilized to merge scaled Voronoi cells, thereby introducing different structural patterns, controlling porosity and to some extent anisotropy. The mechanical properties of the structures were evaluated using analytical estimations, numerical simulations, and experimental compression tests of 3D-printed versions of the structures. The capacity of the developed models to represent trabecular bone was assessed by comparing some key geometric features with trabecular bone characterized in previous studies.

RESULTS

The models gave the possibility to provide pore interconnectivity at relatively low porosities as well as both plate- and rod-like structures. The mechanical properties of the generated models were predictable with numerical simulations as well as an analytical approach. The permeability was found to be better than Sawbones at the same porosity. The models also showed the capability of matching e.g. some vertebral structures for key geometric features.

CONCLUSIONS

An improved numerical model for mimicking trabecular bone structures was successfully developed using Voronoi tessellation and Boolean operations. This is expected to benefit both computational and experimental studies by providing a more diverse and representative structure of trabecular bone.

Approach to standardized material characterization of the human lumbopelvic system-Specification, preparation and storage

The complexity of the osseo-ligamentous lumbopelvic system has made it difficult to perform both, the overall preparation as well as specimen harvesting and material testing with a reasonable amount of time and personnel. The logistics of such studies present a hurdle for reproducibility. A structured procedure was developed and proved, which allows all necessary steps to be carried out reproducibly and in a reasonable time. This enables the extraction of 26 soft tissue, 33 trabecular and 32 cortical bone specimens from this anatomical region per cadaver. The integrity of the specimens remains maintained while keeping requirements within manageable limits. The practicability of the intended five-day specimen harvesting and testing procedure could be demonstrated on five test and two pre-test sequences. The intended minimization of physical, biological, and chemical external influences on specimens could be achieved. All protocols, instructions and models of preparation and storage devices are included in the supporting information. The high grade of applicability and reproducibility will lead to better comparability between different biomechanical investigations. This procedure proven on the human pelvis is transferable to other anatomical regions.

Conceptual design of compliant bone scaffolds by full-scale topology optimization

A promising new treatment for large and complex bone defects is to implant specifically designed and additively manufactured synthetic bone scaffolds. Optimizing the scaffold design can potentially improve bone in-growth and prevent under- and over-loading of the adjacent tissue. This study aims to optimize synthetic bone scaffolds over multiple-length scales using the full-scale topology optimization approach, and to assess the effectiveness of this approach as an alternative to the currently used mono- and multi-scale optimization approaches for orthopaedic applications. We present a topology optimization formulation, which is matching the scaffold's mechanical properties to the surrounding tissue in compression. The scaffold's porous structure is tuneable to achieve the desired morphological properties to enhance bone in-growth. The proposed approach is demonstrated in-silico, using PEEK, cortical bone and titanium material properties in a 2D parameter study and on 3D designs. Full-scale topology optimization indicates a design improvement of 81% compared to the multi-scale approach. Furthermore, 3D designs for PEEK and titanium are additively manufactured to test the applicability of the method. With further development, the full-scale topology optimization approach is anticipated to offer a more effective alternative for optimizing orthopaedic structures compared to the currently used multi-scale methods.

Validation of a novel testing machine for the investigation of the biomechanical properties of lumbar vertebrae in an osteoporotic rat model

BACKGROUND

For the investigation of the biomechanical properties of bone, various testing devices have been described. However, only a limited number have been developed to test the vertebral body of small animals. The aim of this study was to develop and validate a new bone testing device, which investigates the different biomechanical properties in small-animal vertebrae as a whole, three-dimensional unit, respecting its anatomical structure.

METHODS

Thirty-five twelve-week-old female Sprague Dawley rats were utilized. Group 1 was composed of 17 rats with a normal bone metabolism without osteoporosis, while Group 2 consisted of 18 rats with manifest osteoporosis, 8 weeks after ovariectomy. The 5th lumbar vertebra of each animal was tested using the new bone testing device. This device has the ability to be adjusted to the slanted nature of each individual vertebral body and fix the vertebra in a natural position to allow for a non-dislocating axial force application. The device is designed to respect the anatomical three-dimensional shape of the vertebral body, thus avoiding the application of non-anatomic, non-physiological forces and thus preventing a distortion of the biomechanical testing results. The parameters investigated were stiffness, yield load, maximum load and failure load, and the results were compared to current literature values.

RESULTS

The conduction of the biomechanical bone testing of the vertebral bodies with the new device was conductible without any instances of dislocation of the vertebrae or machine malfunctions. Significant differences were found for stiffness, maximum load and failure load between groups, with a lower value in the osteoporotic rats in each parameter tested. The yield load was also lower in the osteoporotic group, however not significantly. The values achieved correlate with those in current literature.

CONCLUSIONS

This study demonstrates that the newly developed testing machine is easy to handle and produces valid data sets for testing biomechanical bone parameters of whole vertebral bodies in an established small animal model. Therefore, it can be utilized, also as reference data, to test different structural properties and changes in vertebral bone, for example, in different metabolic settings or under the influence of different pharmaceutical entities in further studies.

Experimentally characterizing the spatially varying anisotropic mechanical property of cancellous bone via a Bayesian calibration method

Traditional experimental tests for characterizing bone's mechanical properties usually hypothesize a uniaxial stress condition without quantitatively evaluating the influence of spatially varying principal material orientations, which cannot accurately predict the mechanical properties distribution of bones in vivo environment. In this study, a Bayesian calibrating procedure was developed using quantified multiaxial stress to investigate cancellous bone's local anisotropic elastic performance around joints as the spatial variation of main bearing orientations. First, the bone cube specimens from the distal femur of sheep are prepared using traditional anatomical axes. The multiaxial stress state of each bone specimen is calibrated using the actual principal material orientations derived from fabric tensor at different anatomical locations. Based on the calibrated multiaxial stress state, the process of identifying mechanical properties is described as an inverse problem. Then, a Bayesian calibration procedure based on a surrogate constitutive model was developed via multiaxial stress correction to identify the anisotropic material parameters. Finally, a comparison between the experiment and simulation results is discussed by applying the optimal model parameters obtained from the Bayesian probability distribution. Compared to traditional uniaxial methods, our results prove that the calibration based on the spatial variation of the main bearing orientations can significantly improve the accuracy of characterizing regional anisotropic mechanical responses. Moreover, we determine that the actual mechanical property distribution is influenced by complicated mechanical stimulation. This study provides a novel method to evaluate the spatially varying mechanical properties of bone tissues enduring complex mechanical loading accurately and effectively. It is expected to provide more realistic mechanical design targets in vivo for a personalized artificial bone prosthesis in clinical treatment.

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

Denosumab treatment is associated with decreased cortical porosity and increased bone density and strength at the proximal humerus of ovariectomized cynomolgus monkeys

Upper extremity fractures, including those at the humerus, are common among women with postmenopausal osteoporosis. Denosumab was shown to reduce humeral fractures in this population; however, no clinical or preclinical studies have quantified the effects of denosumab on humerus bone mineral density or bone microarchitecture changes. This study used micro-computed tomography (μCT) and computed tomography (CT), alongside image-based finite element (FE) models derived from both modalities, to quantify the effects of denosomab (DMAb) and alendronate (ALN) on humeral bone from acutely ovariectomized (OVX) cynomolgus monkeys. Animals were treated with 12 monthly injections of s.c. vehicle (VEH; n = 10), s.c. denosumab (DMAb; 25 mg/kg, n = 9), or i.v. alendronate (ALN; 50 μg/kg, n = 10). Two more groups received 6 months of VEH followed by 6 months of DMAb (VEH-DMAb; n = 7) or 6 months of ALN followed by 6 months of DMAb (ALN-DMAb; n = 9). After treatment, humeri were harvested and μCT was used to quantify tissue mineral density, trabecular morphology, and cortical porosity at the humeral head. Clinical CT imaging was also used to quantify trabecular and cortical bone mineral density (BMD) at the ultra-proximal, proximal, 1/5 proximal and midshaft of the bone. Finally, μCT-based FE models in compression, and CT-based FE models in compression, torsion, and bending, were developed to estimate differences in strength. Compared to VEH, groups that received DMAb at any time demonstrated lower cortical porosity and/or higher tissue mineral density via μCT; no effects on trabecular morphology were observed. FE estimated strength based on μCT was higher after 12-months DMAb (p = 0.020) and ALN-DMAb (p = 0.024) vs. VEH; respectively, FE predicted mean (SD) strength was 4649.88 (710.58) N, and 4621.10 (1050.16) N vs. 3309.4 (876.09) N. All antiresorptive treatments were associated with higher cortical BMD via CT at the 1/5 proximal and midshaft of the humerus; however, no differences in CT-based FE predicted strength were observed. Overall, these results help to explain the observed reductions in humeral fracture rate following DMAb treatment in women with postmenopausal osteoporosis.

Limit analysis of human proximal femur

A limit analysis numerical approach oriented to predict the peak/collapse load of human proximal femur, under two different loading conditions, is presented. A yield criterion of Tsai-Hu-type, expressed in principal stress space, is used to model the orthotropic bone tissues. A simplified human femur 3D model is envisaged to carry on numerical simulation of in-vitro tests borrowed from the relevant literature and to reproduce their findings. A critical discussion, together with possible future developments, is presented.

Development of a crushable foam model for human trabecular bone

Finite element (FE) simulations can be used to evaluate the mechanical behavior of human bone and allow for quantitative prediction of press-fit implant fixation. An adequate material model that captures post-yield behavior is essential for a realistic simulation. The crushable foam (CF) model is a constitutive model that has recently been proposed in this regard. Compression tests under uniaxial and confined loading conditions were performed on 59 human trabecular bone specimens. Three essential material parameters were obtained as a function of bone mineral density (BMD) to develop the isotropic CF model. The related constitutive rule was implemented in FE models and the results were compared to the experimental data. The CF model provided an accurate simulation of uniaxial compression tests and the post-yield behavior of the stress-strain was well-matched with the experimental results. The model was able to reproduce the confined response of the bone up to 15% of strain. This model allows for simulation of the mechanical behavior of the cellular structure of human bone and adequately predicts the post-yield response of trabecular bone, particularly under uniaxial loading conditions. The model can be further improved to simulate bone collapse due to local overload around orthopaedic implants.

Influence of osteoporosis on the compressive properties of femoral cancellous bone and its dependence on various density parameters

Data collection of mechanical parameters from compressive tests play a fundamental role in FE modelling of bone tissues or the developing and designing of bone implants, especially referring to osteoporosis or other forms of bone loss. A total of 43 cylindrical samples (Ø8 × 16 mm) were taken from 43 freshly frozen proximal femora using a tenon cutter. All femora underwent BMD measurement and additionally apparent- and relative- and bulk density (ρ_app, ρ_r, ρ_b) were determined using samples bordering the compressive specimen on the proximal and distal regions. All samples were classified as "normal", "osteopenia" and "osteoporosis" based on the DEXA measurements. Distal apparent density was most suitable for predicting bone strength and BMD. One novel aspect is the examination of the plateau stress as it describes the stress at which the failure of spongious bone progresses. No significant differences in mechanical properties (compressive modulus E; compressive stress σ_max and plateau stress σ_p) were found between osteopenic and osteoporotic bone. The results suggest that already in the case of a known osteopenia, actions should be taken as they are applied in the case of osteoporosis A review of the literature regarding extraction and testing methods illustrates the urgent need for standardized biomechanical compressive material testing.

Mechanical fatigue of whole rabbit-tibiae under combined compression-torsional loading is better explained by strained volume than peak strain magnitude

The mechanical fatigue behavior of whole bone is poorly defined, particularly for the combined loading modes that occur in vivo. The purpose of this study was to quantify the fatigue life of whole rabbit-tibiae under cyclic uniaxial compression and biaxial (compression and torsion) loading, and to explore the relationship between fatigue life and specimen-specific finite element (FE) predictions of stress/strain. Twelve tibiae were tested cyclically until failure across a range of uniaxial-compressive loads. Another twenty-two tibiae were separated into three groups and loaded biaxially; peak compressive load was constant in all three groups (50% ultimate force) but torsion was varied (0%, 25%, or 50% of ultimate torque). FE models with heterogeneous linear-elastic material properties were developed from computed tomography. We assessed peak stress/strain and stressed/strained volume based on principal stress/strain, as well as von Mises and pressure modified von Mises criteria. A logarithmic (r² = 0.68; p < 0.001) relationship was observed between uniaxial-compressive load and fatigue life. Biaxial tests demonstrated that fatigue life decreased with superposed torsion (p = 0.034). Strained volume, based on a maximum principal strain or pressure modified von Mises strain criteria, were strong predictors of fatigue life under both uniaxial (r² = 0.73-0.82) and biaxial (r² = 0.59-0.60) loads, and these outperformed equivalent peak stress- and strain-based measures. Our findings highlight the importance of evaluating strain distributions, rather than peak stress or strain, to predict the fatigue behavior or whole bone, which has important implications for the study of stress fracture.

Damage tolerance and toughness of elderly human femora

Observations of elastic instability of trabecular bone cores supported the analysis of cortical thickness for predicting bone fragility of the hip in people over 60 years of age. Here, we falsified the hypothesis that elastic instability causes minimal energy fracture by analyzing, with a micrometric resolution, the deformation and fracture behavior of entire femora. Femur specimens were obtained from elderly women aged between 66 - 80 years. Microstructural images of the proximal femur were obtained under 3 - 5 progressively increased loading steps and after fracture. Bone displacements, strain, load bearing and energy absorption capacity were analyzed. Elastic instability of the cortex appeared at early loading stages in regions of peak compression. No elastic instability of trabecular bone was observed. The subchondral bone displayed local crushing in compression at early loading steps and progressed to 8 - 16% compression before fracture. The energy absorption capacity was proportional to the displacement. Stiffness decreased to near-zero values before fracture. Three-fourth of the fracture energy (10.2 - 20.2 J) was dissipated in the final 25% force increment. Fracture occurred in regions of peak tension and shear, adjacent to the location of peak compression, appearing immediately before fracture. Minimal permanent deformation was visible along the fracture surface. Elastic instability modulates the interaction between cortical and trabecular bone promoting an elastically stable fracture behavior of the femur organ, load bearing capacity, toughness, and damage tolerance. These findings will advance current methods for predicting hip fragility.

Functional electrical stimulation (FES)-assisted rowing combined with zoledronic acid, but not alone, preserves distal femur strength and stiffness in people with chronic spinal cord injury

We investigated the effect of 12 months of functional electrical stimulation-assisted rowing with and without zoledronic acid (ZA) on computationally estimated bone strength and stiffness in individuals with spinal cord injury. We found that rowing with ZA, but not rowing alone, improved stiffness at the distal femur, but not the proximal tibia.

INTRODUCTION

People with spinal cord injury (SCI) have high fracture risk at the knee after the injury. Therapies that prevent bone loss or stimulate an anabolic response in bone have been proposed to reduce fractures. Zoledronic acid (ZA) is a potent bisphosphonate that inhibits osteoclastic resorption. Functional electrical stimulation (FES)-assisted rowing is a potentially osteogenic exercise involving mechanical stimulation to the lower extremities. Here, we investigated the effect of FES-assisted rowing with and without ZA on bone strength and stiffness in individuals with SCI.

METHODS

Twenty individuals from a cohort of adults with SCI who participated in a clinical trial were included in the study. CT scans of their knees before and after the intervention were converted to finite element models. Bone failure strength (T_ult) and stiffness were calculated at the proximal tibia and distal femur.

RESULTS

T_ult at the distal femur increased 4.6% among people who received rowing + ZA and decreased 13.9% among those with rowing only (p < 0.05 for group). Torsional and compressive stiffness at the femur metaphysis increased in people with rowing + ZA (+ 3 to +4%) and decreased in people with rowing only (- 7 to -8%; p < 0.05). T_ult in the proximal tibia decreased in everyone, but the loss was attenuated in the rowing + ZA group. People with initially stronger bone tended to lose more strength.

CONCLUSION

Overall, we observed increases in bone strength at the distal femur but not the proximal tibia, with FES-assisted rowing combined with ZA treatment. Rowing alone did not significantly prevent bone loss at either site, which might be attributed to insufficient mechanical loading.

Shear behavior of human skull bones

A shear-punch test (SPT) experimental method was developed to address the lack of shear deformation and failure response data for the human skull as a function of local bone microarchitecture. Improved understanding of skull deformation and fracture under varying stress-states helps implement mechanism-based, multi-axial material models for finite element analysis for optimizing protection strategies. Shear-punch coupons (N = 47 specimens) were extracted from right-parietal and frontal bones of three fresh-frozen-thawed human skulls. The specimens were kept as full through-thickness or segmented into the three skull constituent layers: the inner and outer cortical tables and the middle porous diploë. Micro-computed x-ray tomography (μCT) before and after SPT provided the bone volume fraction (BVF) as a function of depth for correlation to shear mechanisms in the punched volumes. Digital image correlation was used to track displacement of the punch above the upper die to minimize compliance error. Five full-thickness specimens were subjected to partial indentation loading to investigate the process of damage development as a function of BVF and depth. It was determined that BVF dominates the shear yield and ultimate strength of human skull bone, but the imposed uniaxial loading rate (0.001 and 0.1 s^-1) did not have as strong a contribution (p = 0.181-0.806 > 0.05) for the shear yield and ultimate strength of the skull bone layer specimens. Shear yield and ultimate strength data were highly correlated to power law relationships of BVF (R² = 0.917-0.949). Full-thickness and partial loaded SPT experiments indicate the diploë primarily dictates the shear strength of the intact structure.

Numerical analysis of hip fracture due to a sideways fall

The primary purpose of this paper is to outline a methodology for evaluating the likelihood of cortical bone fracture in the proximal femur in the event of a sideways fall. The approach includes conducting finite element (FE) analysis in which the cortical bone is treated as an anisotropic material, and the admissibility of the stress field is validated both in tension and compression regime. In assessing the onset of fracture, two methodologies are used, namely the Critical Plane approach and the Microstructure Tensor approach. The former is employed in the tension regime, while the latter governs the conditions at failure in compression. The propagation of localized damage is modeled using a constitutive law with embedded discontinuity (CLED). In this approach, the localized deformation is described by a homogenization procedure in which the average properties of cortical tissue intercepted by a macrocrack are established. The key material properties governing the conditions at failure are specified from a series of independent material tests conducted on cortical bone samples tested at different orientations relative to the loading direction. The numerical analysis deals with simulations of experiments involving the sideways fall, and the results are compared with the experimental data. This includes both the evolution of fracture pattern and the local load-displacement characteristics. The proposed approach is numerically efficient, and the results do not display a pathological mesh-dependency. Also, in contrast to the XFEM approach, the analysis does not require any extra degrees of freedom.

Cortical thinning and accumulation of large cortical pores in the tibia reflect local structural deterioration of the femoral neck

INTRODUCTION

Cortical bone thinning and a rarefaction of the trabecular architecture represent possible causes of increased femoral neck (FN) fracture risk. Due to X-ray exposure limits, the bone microstructure is rarely measurable in the FN of subjects but can be assessed at the tibia. Here, we studied whether changes of the tibial cortical microstructure, which were previously reported to be associated with femur strength, are also associated with structural deteriorations of the femoral neck.

METHODS

The cortical and trabecular architectures in the FN of 19 humans were analyzed ex vivo on 3D microcomputed tomography images with 30.3 μm voxel size. Cortical thickness (Ct.Th_tibia), porosity (Ct.Po_tibia) and pore size distribution in the tibiae of the same subjects were measured using scanning acoustic microscopy (12 μm pixel size). Femur strength during sideways falls was simulated with homogenized voxel finite element models.

RESULTS

Femur strength was associated with the total (vBMD_tot; R² = 0.23, p < 0.01) and trabecular (vBMD_trab; R² = 0.26, p < 0.01) volumetric bone mineral density (vBMD), with the cortical thickness (Ct.Th_FN; R² = 0.29, p < 0.001) and with the trabecular bone volume fraction (Tb.BV/TV_FN; R² = 0.34, p < 0.001), separation (Tb.Sp_FN; R² = 0.25, p < 0.01) and number (Tb.N_FN; R² = 0.32, p < 0.001) of the femoral neck. Moreover, smaller Ct.Th_tibia was associated with smaller Ct.Th_FN (R² = 0.31, p < 0.05), lower Tb.BV/TV_FN (R² = 0.29, p < 0.05), higher Tb.Sp_FN (R² = 0.33, p < 0.05) and lower Tb.N_FN (R² = 0.42, p < 0.01). A higher prevalence of pores with diameter > 100 μm in tibial cortical bone (relCt.Po_100μm-tibia) indicated higher Tb.Sp_FN (R² = 0.36, p < 0.01) and lower Tb.N_FN (R² = 0.45, p < 0.01).

CONCLUSION

Bone resorption and structural decline of the femoral neck may be identified in vivo by measuring cortical bone thickness and large pores in the tibia.

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

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Femur strength predictions by nonlinear homogenized voxel finite element models reflect the microarchitecture of the femoral neck

In the human femoral neck, the contribution of the cortical and trabecular architecture to mechanical strength is known to depend on the load direction. In this work, we investigate if QCT-derived homogenized voxel finite element (hvFE) simulations of varying hip loading conditions can be used to study the architecture of the femoral neck. The strength of 19 pairs of human femora was measured ex vivo using nonlinear hvFE models derived from high-resolution peripheral QCT scans (voxel size: 30.3 µm). Standing and side-backwards falling loads were modeled. Quasi-static mechanical tests were performed on 20 bones for comparison. Associations of femur strength with volumetric bone mineral density (vBMD) or microstructural parameters of the femoral neck obtained from high-resolution QCT were compared between mechanical tests and simulations and between standing and falling loads. Proximal femur strength predictions by hvFE models were positively associated with the vBMD of the femoral neck (R² > 0.61, p < 0.001), as well as with its cortical thickness (R² > 0.27, p < 0.001), trabecular bone volume fraction (R² = 0.42, p < 0.001) and with the first two principal components of the femoral neck architecture (R² > 0.38, p < 0.001). Associations between femur strength and femoral neck microarchitecture were stronger for one-legged standing than for side-backwards falling. For both loading directions, associations between structural parameters and femur strength from hvFE models were in good agreement with those from mechanical tests. This suggests that hvFE models can reflect the load-direction-specific contribution of the femoral neck microarchitecture to femur strength.

Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra

Quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra are widely used in studying spine biomechanics and mechanobiology, but their accuracy has not been fully established. Although the models typically assign material properties based only on local bone mineral density (BMD), the mechanical behavior of trabecular bone also depends on fabric. The goal of this study was to determine the effect of incorporating measurements of fabric on the accuracy of FE predictions of vertebral deformation. Accuracy was assessed by using displacement fields measured via digital volume correlation-applied to time-lapse microcomputed tomography (μCT)-as the gold standard. Two QCT-based FE models were generated from human L1 vertebrae (n = 11): the entire vertebral body and a cuboid-shaped portion of the trabecular centrum [dimensions: (20-30) × (15-20) × (15-20) mm3]. For axial compression boundary conditions, there was no difference (p = 0.40) in the accuracy of the FE-computed displacements for models using material properties based on local values of BMD versus those using material properties based on local values of fabric and volume fraction. However, when using BMD-based material properties, errors were higher for the vertebral-body models (8.4-50.1%) than cuboid models (1.5-19.6%), suggesting that these properties are inaccurate in the peripheral regions of the centrum. Errors also increased when assuming that the cuboid region experienced uniaxial loading during axial compression of the vertebra. These findings indicate that a BMD-based constitutive model is not sufficient for the peripheral region of the vertebral body when seeking accurate QCT-based FE modeling of the vertebra.

Effect of Multiaxial Tensile Deformation on the Mechanical Properties of Semiflexible Polymeric Samples

Molecular dynamics simulation is used to investigate the mechanical properties of the semiflexible polymer during multiaxial tensile deformations. The multiaxial tensile deformations can be imposed in totally or partially constrained modes. These types of deformations may be observed during the sudden deformation of polymeric material in the areas of aerospace, automobile, defense applications, etc. It is found that the constrained multiaxial deformation leads to the formation of nanovoids into the polymer sample. The high Young's modulus and yield strength for the totally constrained modes of tensile deformation are due to the energy required to create voids. The variation in von Misses stress, void volume, and bond order parameter with strain indicates the occurrence of brittle fracture during totally constrained tensile deformations. The partially constrained tensile deformations lead to the improvement in bond order parameter and lesser creation of nanovoids within the system. The system shows the characteristic strain hardening before failures.

Are we crying Wolff? 3D printed replicas of trabecular bone structure demonstrate higher stiffness and strength during off-axis loading

Roux's principle of bone functional adaptation postulates that bone tissue, and particularly trabecular bone tissue, responds to mechanical stimuli by adjusting (modeling) its architecture accordingly. Hence, it predicts that the new modeled trabecular structure is mechanically improved (stiffer and stronger) in line with the habitual in vivo loading direction. While previous studies found indirect evidence to support this theory, direct support was so far unattainable. This is attributed to the fact that each trabecular bone is unique, and that trabecular bone tissue tends to be damaged during mechanical testing. Consequently, a unique modeled trabecular structure can be mechanically tested only along one direction and a comparison to other directions for that specific structure is impossible. To address this issue, we have 3D printed 10 replicas of a trabecular structure from a sheep talus cropped along the 3 principal axes of the bone and in line with the principal direction of loading (denoted on-axis model). Next, we have rotated the same cropped trabecular structure in increments of 10° up to 90° to the bone principal direction of loading (denoted off-axis models) and printed 10 replicas of each off-axis model. Finally, all on-axis and off-axis 3D printed replicas were loaded in compression until failure and trabecular structure stiffness and strength were calculated. Contrary to our prediction, and conflicting with Roux's principle of bone functional adaptation, we found that a trabecular structure loaded off-axis tended to have higher stiffness and strength values when compared to the same trabecular structure loaded on-axis. These unexpected results may not disprove Roux's principle of bone functional adaptation, but they do imply that trabecular bone adaptation may serve additional purposes than simply optimizing bone structure to one principal loading scenario and this suggests that we still don't fully understand bone modeling in its entirety.

Bisphosphonate treatment changes regional distribution of trabecular microstructure in human lumbar vertebrae

BACKGROUND

In osteoporosis patients, antiresorptive treatments such as alendronate reduce the resorption of trabecular bone and thus minimize vertebral fracture risk. However, fracture risk reduction efficacy of antiresorptive drugs varies between skeletal sites and is highest for vertebral bone. In human vertebrae, cancellous bone is distributed heterogeneously between regions. This microstructural heterogeneity is changing with patient age and is likely to play a major role in vertebral failure mechanisms and fracture susceptibility. Whether antiresorptive treatment affects the heterogeneity of vertebral microstructure in osteoporosis has not been unraveled.

METHODS

Our aim was to assess whether antiresorptive treatment would have a region-dependent influence on vertebral trabecular bone. Therefore, we used high-resolution peripheral quantitative computed tomography (HR-pQCT), microcomputed tomography (microCT) and uniaxial compression testing to determine the structure and mechanical properties of trabecular bone cores from anterior and posterior regions of 22 lumbar vertebrae from elderly osteoporotic women. We analyzed age-matched ex vivo bone samples from bisphosphonate-treated female osteoporosis patients (age: 82 ± 7y, bisphosphonate treatment period: 4 ± 2 years) along treatment-naïve female controls (82 ± 7y).

RESULTS

MicroCT analysis showed a significantly lower bone volume fraction (p = 0.006) and lower trabecular number (p = 0.003) for the anterior bone cores compared to posterior bone cores in the treatment-naïve group. The bisphosphonate-treated group had a more homogeneous bone volume distribution and did not show significant regional differences in bone volume, it however also displayed significantly different trabecular numbers (p = 0.016). In bone cores of the bisphosphonate-treated group, trabeculae were thicker in comparison to treatment-naïve controls (p = 0.011). Differences in bone volume further resulted in different maximum forces during compression testing between the samples. In addition, the percental difference between BV/TV_μCT in anterior and posterior bone cores was lower in bisphosphonate-treated vertebrae when vertebrae with directly adjacent fractures (n = 3) were excluded.

CONCLUSION

In conclusion, regional trabecular bone microstructure in lumbar vertebrae of bisphosphonate-treated women was more homogeneous compared to treatment-naïve controls. Bisphosphonate treatment, which specifically targets resorption surfaces common in anterior vertebral bone, might have resulted in a region-specific preservation of vertebral microstructure and loading capacity. This could have positive implications for the reduction of wedge fracture risk and add to the explanation of the higher efficacy of fracture risk reduction in vertebrae in comparison to other fracture regions.

QCT-based finite element prediction of pathologic fractures in proximal femora with metastatic lesions

Predicting pathologic fractures in femora with metastatic lesions remains a clinical challenge. Currently used guidelines are inaccurate, especially to predict non-impeding fractures. This study evaluated the ability of a nonlinear quantitative computed tomography (QCT)-based homogenized voxel finite element (hvFE) model to predict patient-specific pathologic fractures. The hvFE model was generated highly automated from QCT images of human femora. The femora were previously loaded in a one-legged stance setup in order to assess stiffness, failure load, and fracture location. One femur of each pair was tested in its intact state, while the contralateral femur included a simulated lesion on either the superolateral- or the inferomedial femoral neck. The hvFE model predictions of the stiffness (0.47 < R² < 0.94), failure load (0.77 < R² < 0.98), and exact fracture location (68%) were in good agreement with the experimental data. However, the model underestimated the failure load by a factor of two. The hvFE models predicted significant differences in stiffness and failure load for femora with superolateral- and inferomedial lesions. In contrast, standard clinical guidelines predicted identical fracture risk for both lesion sites. This study showed that the subject-specific QCT-based hvFE model could predict the effect of metastatic lesions on the biomechanical behaviour of the proximal femur with moderate computational time and high level of automation and could support treatment strategy in patients with metastatic bone disease.

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.

Large cortical bone pores in the tibia are associated with proximal femur strength

Alterations of structure and density of cortical bone are associated with fragility fractures and can be assessed in vivo in humans at the tibia. Bone remodeling deficits in aging women have been recently linked to an increase in size of cortical pores. In this ex vivo study, we characterized the cortical microarchitecture of 19 tibiae from human donors (aged 69 to 94 years) to address, whether this can reflect impairments of the mechanical competence of the proximal femur, i.e., a major fracture site in osteoporosis. Scanning acoustic microscopy (12 μm pixel size) provided reference microstructural measurements at the left tibia, while the bone vBMD at this site was obtained using microcomputed tomography (microCT). The areal bone mineral density of both left and right femoral necks (aBMD_neck) was measured by dual‐energy X‐ray absorptiometry (DXA), while homogenized nonlinear finite element models based on high-resolution peripheral quantitative computed tomography provided hip stiffness and strength for one-legged standing and sideways falling loads. Hip strength was associated with aBMD_neck (r = 0.74 to 0.78), with tibial cortical thickness (r = 0.81) and with measurements of the tibial cross-sectional geometry (r = 0.48 to 0.73) of the same leg. Tibial vBMD was associated with hip strength only for standing loads (r = 0.59 to 0.65). Cortical porosity (Ct.Po) of the tibia was not associated with any of the femoral parameters. However, the proportion of Ct.Po attributable to large pores (diameter > 100 μm) was associated with hip strength in both standing (r = -0.61) and falling (r = 0.48) conditions. When added to aBMD_neck, the prevalence of large pores could explain up to 17% of the femur ultimate force. In conclusion, microstructural characteristics of the tibia reflect hip strength as well as femoral DXA, but it remains to be tested whether such properties can be measured in vivo.

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

OBJECTIVES

Dental implants are widely used to restore function and appearance. It may be essential to choose the appropriate drilling protocol and implant design in order to optimise primary stability. This could be achieved based on an assessment of the implantation site with respect to bone quality and objective biomechanical descriptors such as stiffness and strength of the bone-implant system. The aim of this ex vivo study is to relate these descriptors with bone quality, with a pre-implantation indicator of implant stability: pilot-hole drilling force (F_drilling), and with two post-implantation indicators: maximal implantation torque (T_implantation) and resonance frequency analysis (RFA).

METHODS

Eighty trabecular bone specimens were cored from human vertebrae and bovine tibiae. Bone volume fraction (BV/TV), a representative for bone quality, was obtained through micro-computed tomography scans. Implants were kept in controlled laboratory conditions following standard surgical procedures. Forces and torques were recorded and RFA was assessed after implantation. Off-axis compression tests were conducted on the implants until failure. Implant stability was identified by stiffness and ultimate force (F_ultimate). The relationships between BV/TV, Stiffness, F_ultimate and F_drilling, T_implantation, RFA were established.

RESULTS

F_drilling correlated well with BV/TV of the implantation site (r² = 0.81), stiffness (r² = 0.75) and F_ultimate (r² = 0.80). T_implantation correlated better with stiffness (r² = 0.86) and F_ultimate (r² = 0.94) than RFA (r² = 0.77 and r² = 0.74, respectively).

CONCLUSION

Our results indicate that BV/TV and bone-implant stability can be directly estimated by the force needed for the pilot drilling that occurs during the site preparation before implantation. Moreover, implantation torque outperforms RFA for evaluating the mechanical competence of the bone-implant system.

A novel technique with reduced computed tomography exposure to predict vertebral compression fracture: a finite element study based on rat vertebrae

Vertebral compression fractures are a significant clinical issue with an annual incidence of approximately 750,000 cases in the USA alone. Mechanical properties of vertebrae are successfully evaluated through finite element (FE) models based on vertebrae CT. However, clinical drawbacks associated to radiation transmission encouraged to explore the possibility to use selected or reduced portions of the vertebra. The objective of our study was to develop a new procedure to predict vertebral compression fracture from sub-volumes. We reconstructed rat vertebras from micro-CT of thoracic and lumbar groups. Each vertebra was partitioned into three sub-volumes of different axial thickness. FE simulating compression tests were performed on each model to evaluate their failure load and stiffness. Using a power function, a high correlation was found for stiffness and strength. The sub-volume with three fifths thickness had a failure load of 180.7 ± 19.2 N for thoracic and of 209.5 ± 27.4 N for the lumbar vertebra. These values were not significantly different from the values found for the entire vertebra (p > 0.05). Based on our findings, failure loads and stiffnesses obtained with reduced CT scans can be successfully used to predict full vertebral failure. This sub-region analysis and power relationship suggests that one can limit radiation exposure to patients when bone characterization is needed. Graphical abstract Estimated mechanical properties in relation to the extent of the computed tomography reconstruction.

Non-setting, injectable biomaterials containing particulate hydroxyapatite can increase primary stability of bone screws in cancellous bone

BACKGROUND

Fracture fixation in weak bone is still a clinical challenge. Screw augmentation was shown to successfully increase their primary stability. The currently used calcium phosphate or polymeric bone cements, however, present important drawbacks such as induced toxicity and/or impaired bone neo-formation. A new approach to enhance bone screw primary stability without affecting bone formation is the use of non-setting, calcium phosphate loaded soft materials as the augmentation material.

METHODS

Two types of biomaterials (non-crosslinked hyaluronic acid as viscous fluid and agar as hydrogel) were loaded with 40 wt/vol% of hydroxyapatite particles and characterized. The screw augmentation effect of all materials was evaluated through pull-out tests in bovine cancellous bone and compared to the non-augmented situation (control). The bone mineral density of each test sample was measured with μCT scans and was used to normalize the pull-out strength.

FINDINGS

Both materials loaded with hydroxyapatite increased the normalized pull-out strength of the screws compared to control samples and particle-free materials. This counter-intuitive augmentation effect increased with decreasing bone mineral density and was independent from the type of the soft materials used.

INTERPRETATION

We were able to demonstrate that non-setting, injectable biomaterials loaded with ceramic particles can significantly enhance the primary stability of bone screws. This material combination opens the unique possibility to achieve a screw augmentation effect without impairing or even potentially favoring the bone formation in proximity to the screw. This effect would be particularly advantageous for the treatment of osteoporotic bone fractures requiring a stabilization with bone screws.

Mechanical loading, an important factor in the evaluation of ion release from bone augmentation materials

The controlled release of therapeutic inorganic ions from biomaterials is an emerging area of international research. One of the foci for this research is the development of materials, which spatially and temporally modulate therapeutic release, via controlled degradation in the intended physiological environment. Crucially however, our understanding of the release kinetics for such systems remains limited, particularly with respect to the influence of physiological loading. Consequently, this study was designed to investigate the effect of dynamic mechanical loading on a composite material intended to stabilize, reinforce and strengthen vertebral bodies. The composite material contains a borate glass engineered to release strontium as a therapeutic inorganic ion at clinically relevant levels over extended time periods. It was observed that both cyclic (6 MPa 2 Hz) and static (4.3 MPa) compressive loading significantly increased the release of strontium ions in comparison to the static unloaded case. The observed alterations in ion release kinetics suggest that the mechanical loading of the implantation environment should be considered when evaluating the ion release kinetics.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

Circum-menarcheal bone acquisition is stress-driven: A longitudinal study in adolescent female gymnasts and non-gymnasts

Mechanical loading through youth exercise is highly modifiable and represents a strategy to maximize peak adult bone mass, with the potential for broad implementation across the population to lower fracture risk. For girls, circum-menarcheal growth is critical, with around 50% of adult bone acquired over a 4-year period. Here, we prospectively followed 10 gymnasts and 12 age-matched non-gymnasts across approximately 4 years circum-menarche. A combination of pQCT and subject-specific finite element models were used to measure differences in bone acquisition and structure between the groups, and to determine the degree to which specific mechanical factors predict change in bone structure. At baseline, gymnasts had stronger bone, including 26% higher BMC, 51% greater compressive strength, and 21% higher trabecular density. Over the study period, both groups more than doubled their bone strength. Pre-menarcheal principal stresses predicted change in pQCT variables for non-gymnasts, but not gymnasts. The bone of non-gymnasts became more asymmetrical than the bone of gymnasts. Our results suggest that exposure to the diverse, intense mechanical signals of gymnastic loading during adolescence imparts substantial benefits to bone geometry and mechanical function. Specifically, the bone of gymnasts is better able to resist loading from multiple directions, and operates with a higher factor of safety compared to non-gymnasts.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

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.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

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.

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.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.