Computational study of estimating 3D trabecular bone microstructure for the volume of interest from CT scan data

Computational comparison study of virtual compression and shear test for estimation of apparent elastic moduli under various boundary conditions

Virtual compression tests based on finite element analysis are representative noninvasive methods to evaluate bone strength. However, owing to the characteristic porous structure of bones, the material obtained from micro-computed tomography images in the finite-element model is not uniformly distributed. These characteristics cause differences in the apparent elastic moduli depending on the boundary conditions and affect the accuracy of bone-strength evaluation. Therefore, this study aimed to evaluate and compare the apparent elastic moduli under various, virtual-compression and shear-test boundary conditions. Four, nonuniform models were constructed with increasing model complexity. For representative boundary conditions, two, different, testing directions, and constrained surfaces were applied. As a result, the apparent elastic moduli of the nonuniform model varied up to 55.2% based on where the constrained surface was located in the single-end-cemented condition. Additionally, when connectivity in the test direction was lost, the accuracy of the apparent elastic moduli was low. A graphical comparison showed that the equivalent-stress distribution was more advantageous for analyzing load transferability and physical behavior than the strain-energy distribution. These results clearly show that the prediction accuracy of the apparent elastic moduli can be guaranteed if the boundary condition on the constraint and loading surfaces of the nonuniform model are applied symmetrically and the connectivity of the elements in the testing direction is well maintained. This study will aid in precision improvement of bone-strength-indicator determination for osteoporosis prevention.

Biomechanical analysis of combi-hole locking compression plate during fracture healing: A numerical study of screw configuration

Locking compression plates (LCPs) have become a widely used option for treating femur bone fractures. However, the optimal screw configuration with combi-holes remains a subject of debate. The study aims to create a time-dependent finite element (FE) model to assess the impacts of different screw configurations on LCP fixation stiffness and healing efficiency across four healing stages during a complete fracture healing process. To simulate the healing process, we integrated a time-dependent callus formation mechanism into a FE model of the LCP with combi-holes. Three screw configuration parameters, namely working length, screw number, and screw position, were investigated. Increasing the working length negatively affected axial stiffness and healing efficiency (p < 0.001), while screw number or position had no significant impact (p > 0.01). The time-dependent model displayed a moderate correlation with the conventional time-independent model for axial stiffness and healing efficiency (ρ ≥ 0.733, p ≤ 0.025). The highest healing efficiency (95.2%) was observed in screw configuration C125 during the 4-8-week period. The results provide insights into managing fractures using LCPs with combi-holes over an extended duration. Under axial compressive loading conditions, the use of the C125 screw configuration can enhance callus formation during the 4-12-week period for transverse fractures. When employing the C12345 configuration, it becomes crucial to avoid overconstraint during the 4-8-week period.

Application of Microfracture Analysis to Fatigue Fractures in Materials through Non-Destructive Tests

Fatigue fractures in materials are the main cause of approximately 80% of all material failures, and it is believed that such failures can be predicted and mathematically calculated in a reliable manner. It is possible to establish prediction modalities in cases of fatigue fractures according to three fundamental variables in fatigue, such as volume, number of fracture cycles, as well as applied stress, with the integration of Weibull constants (length characteristic). In this investigation, mechanical fatigue tests were carried out on specimens smaller than 4 mm2, made of different industrial materials. Their subsequent analysis was performed through precision computed tomography, in search for microfractures. The measurement of these microfractures, along with their metrics and classifications, was recorded. A convolutional neural network trained with deep learning was used to achieve the detection of microfractures in image processing. The detection of microfractures in images with resolutions of 480 × 854 or 960 × 960 pixels is the primary objective of this network, and its accuracy is above 95%. Images that have microfractures and those without are classified using the network. Subsequently, by means of image processing, the microfracture is isolated. Finally, the images containing this feature are interpreted using image processing to obtain their area, perimeter, characteristic length, circularity, orientation, and microfracture-type metrics. All values are obtained in pixels and converted to metric units (μm) through a conversion factor based on image resolution. The growth of microfractures will be used to define trends in the development of fatigue fractures through the studies presented.

An Analysis of Trabecular Bone Structure Based on Principal Stress Trajectory

To understand the mechanism of Wolff's law, a finite element analysis was performed for a human proximal femur, and the principal stress trajectories of the femur were extracted using the principal stress visualization method. The mechanism of Wolff's law was evaluated theoretically based on the distribution of the principal stress trajectories. Due to the dynamics of the loads, there was no one-to-one correspondence between the stress trajectories of the fixed load and the trabeculae in the cancellous architecture of the real bone. The trabeculae in the cancellous bone were influenced by the magnitude of the principal stress trajectory. Equivalent principal stress trajectories suitable for different load changes were proposed through the change in load cycle and compared with the anatomical structure of the femur. In addition, the three-dimensional distribution of the femoral principal stress trajectory was established, and the adaptability potential of each load was discussed. The principal stress visualization method could also be applied to bionic structure design.

Detection of defects in cellular solids using highly nonlinear solitary waves: a numerical study of the proximal femur

This study investigates the suitability of a relatively new non-destructive evaluation (NDE) technique for the detection of non-visible defects in cellular solids using highly nonlinear solitary waves (HNSWs) in a one-dimensional granular chain. Specifically, the HNSW-based NDE approach is employed to identify the existence of micro-fractures in trabecular bone within the femoral neck (FN) and the intertrochanteric (IT) region of the proximal femur which are fracture-prone sites due to their relatively low bone density, particularly in osteoporosis patients. The availability of a HNSW-based bone quality assessment tool could not only help in early diagnosis of osteoporosis but also affect surgical decisions and improve clinical outcomes in joint replacement surgeries which motivated this study. To obtain a realistic representation of the trabecular microstructure, high-resolution finite-element (FE) models of the FN and the IT region are first constructed using a topology optimization-based bone reconstruction scheme. Then, artificial defects in the form of fractured ligaments are generated in the FN and IT models by selectively disconnecting various struts within the trabecular network. Using the FE models as the inspection medium, hybrid discrete-element/finite-element (DE/FE) simulations are performed to examine the interaction of the HNSWs with the cellular bone samples through two different inspection modes, i.e., inspection via direct contact with the sample and indirect contact through an adequately chosen face sheet inserted between the cellular sample and the granular chain. The delays and amplitudes of the HNSWs are used to estimate the effective elastic moduli of the cellular samples and these estimates were found to be reasonably accurate only in case the face sheet was applied. For the latter case, it was shown that the HNSW-based modulus estimates can be used as indicators for defect detection, allowing to discern between pristine and damaged cellular solids. These results suggest that HNSW-based NDE is a reliable and cost-effective technique for the identification of defects in cellular solids, and is expected to find applications in various fields, such as non-invasive screening of bone diseases and fractures, or damage detection in additively manufactured cellular structures.

Topology Optimization-Based Localized Bone Microstructure Reconstruction for Image Resolution Enhancement: Accuracy and Efficiency

Topology optimization is currently the only way to provide bone microstructure information by enhancing a 600 μm low-resolution image into a 50 μm high-resolution image. Particularly, the recently proposed localized reconstruction method for the region of interest has received much attention because it has a high possibility to overcome inefficiency such as iterative large-scale problems of the conventional reconstruction. Despite the great potential, the localized method should be thoroughly validated for clinical application. This study aims to quantitatively validate the topology optimization-based localized bone microstructure reconstruction method in terms of accuracy and efficiency by comparing the conventional method. For this purpose, this study re-constructed bone microstructure for three regions of interest in the proximal femur by localized and conventional methods, respectively. In the comparison, the dramatically reduced total progress time by at least 88.2% (20.1 h) as well as computational resources by more than 95.9% (54.0 gigabytes) were found. Moreover, very high reconstruction accuracy in the trabecular alignment (up to 99.6%) and morphometric indices (up to 2.71%) was also found. These results indicated that the localized method could reconstruct bone microstructure, much more effectively preserving the originality of the conventional method.

Predictions of the elastic modulus of trabecular bone in the femoral head and the intertrochanter: a solitary wave-based approach

This paper deals with the numerical prediction of the elastic modulus of trabecular bone in the femoral head (FH) and the intertrochanteric (IT) region via site-specific bone quality assessment using solitary waves in a one-dimensional granular chain. For accurate evaluation of bone quality, high-resolution finite element models of bone microstructures in both FH and IT are generated using a topology optimization-based bone microstructure reconstruction scheme. A hybrid discrete element/finite element (DE/FE) model is then developed to study the interaction of highly nonlinear solitary waves in a granular chain with the generated bone microstructures. For more robust and reliable prediction of the bone's mechanical properties, a face sheet is placed at the interface between the last chain particle and the bone microstructure, allowing more bone volume to be engaged in the dynamic deformation during interaction with the solitary wave. The hybrid DE/FE model was used to predict the elastic modulus of the IT and FH by analysing the characteristic features of the two primary reflected solitary waves. It was found that the solitary wave interaction is highly sensitive to the elastic modulus of the bone microstructure and can be used to identify differences in bone density. Moreover, it was found that the use of a relatively stiff face sheet significantly reduces the sensitivity of the wave interaction to local stiffness variations across the test surface of the bone, thereby enhancing the robustness and reliability of the proposed method. We also studied the effect of the face sheet thickness on the characteristics of the reflected solitary waves and found that the optimal thickness that minimizes the error in the modulus predictions is 4 mm for the FH and 2 mm for the IT, if the primary reflected solitary wave is considered in the evaluation process. We envisage that the proposed diagnostic scheme, in conjunction with 3D-printed high-resolution bone models of an actual patient, could provide a viable solution to current limitations in site-specific bone quality assessment.

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

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

Patient-Specific Phantomless Estimation of Bone Mineral Density and Its Effects on Finite Element Analysis Results: A Feasibility Study

Objectives

This study proposes a regression model for the phantomless Hounsfield units (HU) to bone mineral density (BMD) conversion including patient physical factors and analyzes the accuracy of the estimated BMD values.

Methods

The HU values, BMDs, circumferences of the body, and cross-sectional areas of bone were measured from 39 quantitative computed tomography images of L2 vertebrae and hips. Then, the phantomless HU-to-BMD conversion was derived using a multiple linear regression model. For the statistical analysis, the correlation between the estimated BMD values and the reference BMD values was evaluated using Pearson's correlation test. Voxelwise BMD and finite element analysis (FEA) results were analyzed in terms of root-mean-square error (RMSE) and strain energy density, respectively.

Results

The HU values and circumferences were statistically significant (p < 0.05) for the lumbar spine, whereas only the HU values were statistically significant (p < 0.05) for the proximal femur. The BMD values estimated using the proposed HU-to-BMD conversion were significantly correlated with those measured using the reference phantom: Pearson's correlation coefficients of 0.998 and 0.984 for the lumbar spine and proximal femur, respectively. The RMSEs of the estimated BMD values for the lumbar spine and hip were 4.26 ± 0.60 (mg/cc) and 8.35 ± 0.57 (mg/cc), respectively. The errors of total strain energy were 1.06% and 0.91%, respectively.

Conclusions

The proposed phantomless HU-to-BMD conversion demonstrates the potential of precisely estimating BMD values from CT images without the reference phantom and being utilized as a viable tool for FEA-based quantitative assessment using routine CT images.

Fully automated segmentation of a hip joint using the patient-specific optimal thresholding and watershed algorithm

BACKGROUND AND OBJECTIVE

Automated segmentation with high accuracy and speed is a prerequisite for FEA-based quantitative assessment with a large population. However, hip joint segmentation has remained challenging due to a narrow articular cartilage and thin cortical bone with a marked interindividual variance. To overcome this challenge, this paper proposes a fully automated segmentation method for a hip joint that uses the complementary characteristics between the thresholding technique and the watershed algorithm.

METHODS

Using the golden section method and load path algorithm, the proposed method first determines the patient-specific optimal threshold value that enables reliably separating a femur from a pelvis while removing cortical and trabecular bone in the femur at the minimum. This provides regional information on the femur. The watershed algorithm is then used to obtain boundary information on the femur. The proximal femur can be extracted by merging the complementary information on a target image.

RESULTS

For eight CT images, compared with the manual segmentation and other segmentation methods, the proposed method offers a high accuracy in terms of the dice overlap coefficient (97.24 ± 0.44%) and average surface distance (0.36 ± 0.07 mm) within a fast timeframe in terms of processing time per slice (1.25 ± 0.27 s). The proposed method also delivers structural behavior which is close to that of the manual segmentation with a small mean of average relative errors of the risk factor (4.99%).

CONCLUSION

The segmentation results show that, without the aid of a prerequisite dataset and users' manual intervention, the proposed method can segment a hip joint as fast as the simplified Kang (SK)-based automated segmentation, while maintaining the segmentation accuracy at a similar level of the snake-based semi-automated segmentation.