Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level

Effect of trabecular architectures on the mechanical response in osteoporotic and healthy human bone

Research at the mesoscale bone trabeculae arrangement yields intriguing results that, due to their clinical resolution, can be applied in clinical field, contributing significantly to the diagnosis of bone-related diseases. While the literature offers quantitative morphometric parameters for a thorough characterization of the mesoscale bone network, there is a gap in understanding relationships among them, particularly in the context of various bone pathologies. This research aims to bridge these gaps by offering a quantitative evaluation of the interplay among morphometric parameters and mechanical response at mesoscale in osteoporotic and non-osteoporotic bones. Bone mechanical response, dependent on trabecular arrangement, is defined by apparent stiffness, computationally calculated using the Gibson-Ashby model. Key findings indicate that: (i) in addition to bone density, measured using X-ray absorptiometry, trabecular connectivity density, trabecular spacing and degree of anisotropy are crucial parameters for characterize osteoporosis state; (ii) apparent stiffness values exhibit strong correlations with bone density and connectivity density; (iii) connectivity density and degree of anisotropy result the best predictors of mechanical response. Despite the inherent heterogeneity in bone structure, suggesting the potential benefit of a larger sample size in the future, this approach presents a valuable method to enhance discrimination between osteoporotic and non-osteoporotic samples.

Preventing stress singularities in peri-implant bone - a finite element analysis using a graded bone model

In finite element analysis bone is often treated as two-layered material that has a discontinuity between the cortical and cancellous bone, which leads to a singularity and incorrect stresses. The goal of this study was to eliminate this singularity and to create a more realistic representation of bone which also considers the transition zone between cortical and cancellous bone as observed in natural bone. This was achieved by modelling bone as a graded material and inserting node-specific values for Young's modulus in the finite element simulation, whereas the transition zone thickness was derived from a CT scan. The modelling was performed semi-automatically, and the maximum principal stresses of the new approach were compared to those of a conventional approach. The new approach was found to effectively avoid singularities and provides more accurate predictions of stress in areas of the bone transition zone. As the approach is automatable and causes rather small overhead it is recommended for use in future work, when the problem at hand requires evaluating stresses close to the former singularity.

High-resolution local trabecular strain within trabecular structure under cyclic loading

Trabecular bone structure is a complex microstructure consisting of rods and plates, which poses challenges for its mechanical characterization. Digital image correlation (DIC) offers the possibility to characterize the strain response on the surface of trabecular bone. This study employed DIC equipped with a telecentric lens to investigate the strain state of individual trabeculae within their trabecular structure by assessing the longitudinal strain of the trabeculae at both the middle and near the edges of the trabeculae. Due to the high-resolution of the used DIC system, local surface strain of trabeculae was analyzed too. Lastly, the correlation between longitudinal trabecular strain and the orientation and slenderness of the trabeculae was investigated. The results showed that the strain magnification close to the edge of the trabeculae was higher and reached up to 8-folds the strain along the middle of the trabeculae. On the contrary, no strain magnification was found for most of the trabeculae between the longitudinal trabecular strain along the middle of the trabeculae and the globally applied strain. High-resolution full-field strain maps were obtained on the surface of trabeculae showing heterogeneous strain distribution with increasing load. No significant correlation was found between longitudinal trabecular strain and its orientation or slenderness. These findings and the applied methodology can be used to broaden our understanding of the deformation mechanisms of trabeculae within the trabecular network.

Exploring the micromorphological characteristics of adult lower cervical vertebrae based on micro-computed tomography

We will use micro-computed tomography to scan 31 sets of the adult lower cervical vertebrae (155 vertebrae) to observe the morphological characteristics and direction of trabeculae in the lower cervical vertebrae by outlining and reconstructing the regions of interest and to calculate the variation laws of the microstructure in the regions of interest to reveal their structural characteristics and weak areas. As a result, the images showed that the trabeculae in the lower cervical pedicle near the medial and lateral cortices were relatively dense, and their bone plates were lamellar. There were cavities between the superior and inferior articular processes where the ossification centers had not been absorbed after ossified. The lamellar trabeculae in the vertebral plates near the cortical bones were only 1-2 layers, extended and transformed into rod-shaped trabeculae in a radial shape toward the medullary space. The lamellar trabeculae of the vertebral plate extend over the spinous process near the cortical bone. The statistical results of the trabeculae's morphological parameters showed significant differences in bone volume fraction values among the four parts (P < 0.05). There were substantial differences in BS/BV, except for no differences between the pedicle and the vertebral plate (P < 0.05). There was a significant difference in trabecular pattern factor values between the articular process, the spinous process, and the vertebral plate (P < 0.05) and a significant difference between the pedicle, the spinous process, and the vertebral plate (P < 0.05). There were no significant differences in trabecular bone thickness and trabecular space values among the four parts (P < 0.05). The anatomical microstructural perspective confirms that the optimal choice is internal fixation via the pedicle. If using pedicle screws, the nail tract needs to be placed into the spinous process to increase its holding power and resistance to extraction.

A New Microarchitecture-Based Parameter to Predict the Micromechanical Properties of Bone Allografts

Scaffolds are an essential component of bone tissue engineering. They provide support and create a physiological environment for cells to proliferate and differentiate. Bone allografts extracted from human donors are promising scaffolds due to their mechanical and structural characteristics. Bone microarchitecture is well known to be an important determinant of macroscopic mechanical properties, but its role at the microscopic, i.e., the trabeculae level is still poorly understood. The present study investigated linear correlations between microarchitectural parameters obtained from X-ray computed tomography (micro-CT) images of bone allografts, such as bone volume fraction (BV/TV), degree of anisotropy (DA), or ellipsoid factor (EF), and micromechanical parameters derived from micro-finite element calculations, such as mean axial strain (ε_z) and strain energy density (W_e). DAEF, a new parameter based on a linear combination of the two microarchitectural parameters DA and EF, showed a strong linear correlation with the bone mechanical characteristics at the microscopic scale. Our results concluded that the spatial distribution and the plate-and-rod structure of trabecular bone are the main determinants of the mechanical properties of bone at the microscopic level. The DAEF parameter could, therefore, be used as a tool to predict the level of mechanical stimulation at the local scale, a key parameter to better understand and optimize the mechanism of osteogenesis in bone tissue engineering.

Measuring Young's modulus of single trabeculae in cancellous bone using a two-point bending test

BACKROUND

Surgical treatment of proximal humeral fractures poses a major challenge, especially in osteoporotic bone. At present, there appears to exist neither a suitable model for research to optimize the osteosynthesis processes nor are the structural data available which are required for developing such a model. Therefore, the aim of this study is to determine the microscopic morphology and Young's modulus of cancellous bone from human humeral heads considering osteoporotic changes.

METHODS

Cylindrical samples were taken from ten fresh-frozen human humeral heads and structural analysis was done with μCT. Ten rod-like trabeculae were prepared from five of the humeral heads each which were measured and tested mechanically. For this purpose, the trabeculae were fixed on a slide and rotated axially under a stereo microscope. The sample cross-section and the depending moment of inertia were extracted from the image data. The samples were then loaded in a 2-point bending test and Young's moduli of the samples were determined.

RESULTS

It could be shown that with increasing age of the donor, ossified portion of the cancellous bone decreased (p < 0.05). The average degree of mineralization of the bone was 1.24 (±0.06) g/mm³, which decreased with increasing age (p < 0.05). The determined Young's modulus averaged 1.33 (±1.76) GPa.

INTERPRETATION

The verified structural parameter showed osteoporotic changes in the examined bone. This study for the first time determined Young's modulus of single trabeculae of cancellous bone of osteoporotically altered human humeral heads. Implementing the non-destructive sample measurement before exposure resulted in a methodical improvement.

A Review of Conventional and Novel Treatments for Osteoporotic Hip Replacements

INTRODUCTION

Osteoporosis is a skeletal disease that severely affects the mechanical properties of bone. It increases the porosity of cancellous bone and reduces the resistance to fractures. It has been reported in 2009 that there are approximately 500 million osteoporotic patients worldwide. Patients who suffer fractures due to fragility cost the National Healthcare Systems in the United Kingdom £4.4 billion in 2018, in Europe €56 billion in 2019, and in the United States $57 billion in 2018. Thus, osteoporosis is problematic for both patients and healthcare systems.

AIM

This review is conducted for the purpose of presenting and discussing all articles introducing or investigating treatment solutions for osteoporotic patients undergoing total hip replacement.

METHODS

Searches were implemented using three databases, namely Scopus, PubMed, and Web of Science to extract all relevant articles. Predetermined eligibility criteria were used to exclude articles out of the scope of the study.

RESULTS

29 articles out of 183 articles were included in this review. These articles were organised into three sections: (i) biomechanical properties and structure of osteoporotic bones, (ii) hip implant optimisations, and (iii) drug, cells, and bio-activators delivery through hydrogels.

DISCUSSION

The findings of this review suggest that diagnostic tools and measurements are crucial for understanding the characteristics of osteoporosis in general and for setting patient-specific treatment plans. It was also found that attempts to overcome complications associated with osteoporosis included design optimisation of the hip implant; however, only short-term success was reported, while the long-term stability of implants was compromised by the progressive nature of osteoporosis. Finally, it was also found that targeting implantation sites with cells, drugs, and growth factors has been outworked using hydrogels, where promising results have been reported regarding enhanced osteointegration and inhibited bacterial and osteoclastic activities.

CONCLUSIONS

These results may encourage investigations that explore the effects of these impregnated hydrogels on osteoporotic bones beyond metallic scaffolds and implants.

Examination of the microstructures of the lower cervical facet based on micro-computed tomography: A cadaver study

The cervical facet has complicated 3D microstructures and inhomogeneities. The cervical facet joint, which also participates in the formation, plays a certain role in regulating and limiting the movement of the spine. Correct identification and evaluation of its microstructure can help in the diagnosis of orthopedic disease and predict early phases of fracture risk. To evaluate the safety of the cervical spine by measuring and analyzing the microstructures and morphometric parameters of bone trabeculae in the normal cervical facet with high-resolution 3D micro-computed tomography. Thirty-one sets of C3 to C7 lower cervical vertebrae (155 vertebrae) were scanned using micro-computed tomography. The morphological characteristics and direction of trabecular bone in the facet of the lower cervical vertebrae were observed by selecting and rebuilding the areas of interest, and the changes in the microstructure of the areas of interest were calculated to reveal the structural characteristics and weak areas. Images indicated an ossified center between the superior and inferior articular processes of the lower cervical spine. The cellular bone trabeculae of the articular process had complex reticular microstructures. The trabecular bone plate near the cortical bone was lamellar and relatively dense, and it extended around and transformed into a network structure, and then into the rod-shaped trabecular bone. The rod-shaped trabeculae converged with the plate-shaped trabeculae with only 1 to 2 layers surrounding the trabeculae cavity. Statistical results of the morphological parameters of the trabecular bone showed that trabecular bone volume fraction values were significantly higher for C7 than for C3 to C6 (P < .05). There were significant differences between C7 and C3 to C5 and between C6 and C4 in bone surface area/bone volume (P < .05). There was a significant difference between C7 and C3 to C6 in trabecular bone thickness values (P < .05). The degree of anisotropy value was significantly smaller for C3 than for C6 and C7 (P < .05). The changes in the C3 to C7 microstructure were summarized in this study. The loading capacity and stress of the C7 articular process tended to be limited, and the risk of injury tended to be higher for the C7 articular process.

Micro-Computed Tomography Analysis of Femoral Head Necrosis After Long-Term Internal Fixation for Femoral Neck Fracture

OBJECTIVE

To analyze necrotic femoral head after long-term internal fixation for femoral neck fractures using micro-computed tomography (CT) for bone histomorphometry.

METHODS

The experimental group included six patients (two men and four women; mean age 62.00 ± 9.36 years) who underwent hip arthroplasty at 47.67 ± 14.22 months after internal fixation. Surgery was performed because of femoral head necrosis after femoral neck fracture between October 2018 and October 2020. The control group included three patients (two men and one woman; mean age 69.33 ± 4.62 years) who underwent hip arthroplasty for femoral neck fracture. In the experimental group, micro-CT quantitative analysis of the whole femur, sclerotic region around screws, screw paths, sclerotic region and screw paths, and relatively normal region was performed. The bone volume fraction (BV/TV), number of bone trabeculae (Tb.N), connection density (Conn.D), thickness of bone trabeculae (Tb.Th), separation of bone trabeculae (Tb.SP), structural model index (SMI), and bone mineral density (BMD) of each part were quantitatively analyzed.

RESULTS

The BV/TV (0.3180 ± 0.0617), Conn.D (6.9261 ± 2.4715/mm3 ), Tb.Th (0.3262 ± 0.0136 μm), and BMD (298.9241 ± 54.2029 g/cm3 ) of the sclerotic region around the screws were significantly higher in the experimental group than the BV/TV (0.1248 ± 0.0390), Conn.D (2.5708 ± 0.5187/mm3 ), Tb.Th (0.1713 ± 0.0333 μm), and BMD (66.5181 ± 43.0380 g/cm3 ) in the control group (P < 0.05). The BV/TV (0.2222 ± 0.0684), Tb.Th (0.2775 ± 0.0326 μm), and BMD (195.0153 ± 71.8509 g/cm3 ) in the collapsed region were significantly higher in the experimental group than in the control group (P < 0.05). In the experimental group, the volume ratio of the sclerotic region around screws and screw paths to the entire femoral head was 0.4964 ± 0.0950.

CONCLUSION

After internal fixation for femoral neck fracture, a large number of sclerotic plate-like trabeculae were observed around the long-term retained implant. The screw paths and surrounding sclerotic comprise approximately 50% of the femoral head volume.

Biomechanical evaluation of the stability of extra-articular distal radius fractures fixed with volar locking plates according to the length of the distal locking screw

Surgeons usually used short screws to avoid extensor tendon problems during volar locking plate fixation in distal radius fracture. However, the stability according to the length of distal locking screws have not been fully understood. We investigated this issue through finite element analysis and compression test using synthetic radius. Our results demonstrated that the bi-cortical full-length fixation does not contribute to the stiffness increase in the axial compression direction, and a reduction in length of up to more than 50% length can still provide similar stability to full-length screws. Our data can support that surgeon should undersize the distal screw.

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.

Age-Related Trends in the Trabecular Micro-Architecture of the Medial Clavicle: Is It of Use in Forensic Science?

The mechanical and structural properties of bone are known to change significantly with age. Within forensic and archaeological investigations, the medial end of the clavicle is typically used for estimating the age-at-death of an unknown individual. Although, this region of the skeleton is of interest to forensic and clinical domains, alterations beyond the macro-scale have not been fully explored. For this study, non-destructive micro-computed tomography (μ-CT) was employed to characterize structural alterations to the cancellous bone of the medial clavicle. Fresh human cadaveric specimens (12-59 years) obtained at autopsy were utilized for this study, and were scanned with a voxel size of ~83 μm. Morphometric properties were quantified and indicated that the bone volume, connectivity density, mineral density, and number of trabeculae decreased with age, while the spacing between the trabeculae increased with age. In contrast to other sub-regions of the skeleton, trabecular thickness, and degree of anisotropy did not correlate with age. Collectively, this could suggest that the network is becoming increasingly perforated with age rather than exhibiting trabecular thinning. These results are used in the context of deriving a potential protocol for forensic investigations by using this particular and largely unexplored region of the skeleton, and provide inspiration for future experiments concerning micro-architectural and small scale changes in other regions of the human skeleton.