Comparison of micro-level and continuum-level voxel models of the proximal femur

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.

The role of torsional stress in the development of subchondral insufficiency fracture of the femoral head: A finite element model analysis

BACKGROUND

Subchondral insufficiency fracture of the femoral head generally occurs without evidence of trauma or with a history of minor trauma. Insufficient bone quality is considered one cause; however, the detailed mechanism of fracture development at the subchondral area (SA) is not understood. The aim of this study was to clarify the directions of force that cause subchondral fracture using finite element model analysis.

METHODS

Two types of finite element models were generated from the CT data of femurs obtained from three individuals without osteoporosis (normal models) and another three with osteoporosis (osteoporosis models). Three directions of force, including compressive, shearing, and torsional, were applied to the femoral head. The distribution of von Mises stress (Mises stress) was evaluated at the SA, principal compressive trabeculae (PC), and principal tensile trabeculae.

RESULTS

Under compressive force, the mean Mises stress value was greatest at the PC in both the normal and osteoporosis models. Under shearing force, the mean Mises stress value tended to be greatest at the SA in the normal model and at the PC in the osteoporosis model. Under torsional force, the mean Mises stress value was greatest at the SA in both types of models.

CONCLUSIONS

The torsional force showed the greatest Mises stress at the SA in both the normal and osteoporosis models, suggesting the importance of torsion as a possible force responsible for subchondral insufficiency fracture development.

Assessing the risk of re-fracture related to the percentage of partial union in scaphoid waist fractures

Aims

There is ambiguity surrounding the degree of scaphoid union required to safely allow mobilization following scaphoid waist fracture. Premature mobilization could lead to refracture, but late mobilization may cause stiffness and delay return to normal function. This study aims to explore the risk of refracture at different stages of scaphoid waist fracture union in three common fracture patterns, using a novel finite element method.

Methods

The most common anatomical variant of the scaphoid was modelled from a CT scan of a healthy hand and wrist using 3D Slicer freeware. This model was uploaded into COMSOL Multiphysics software to enable the application of physiological enhancements. Three common waist fracture patterns were produced following the Russe classification. Each fracture had differing stages of healing, ranging from 10% to 90% partial union, with increments of 10% union assessed. A physiological force of 100 N acting on the distal pole was applied, with the risk of refracture assessed using the Von Mises stress.

Results

Overall, 90% to 30% fracture unions demonstrated a small, gradual increase in the Von Mises stress of all fracture patterns (16.0 MPa to 240.5 MPa). All fracture patterns showed a greater increase in Von Mises stress from 30% to 10% partial union (680.8 MPa to 6,288.6 MPa).

Conclusion

Previous studies have suggested 25%, 50%, and 75% partial union as sufficient for resuming hand and wrist mobilization. This study shows that 30% union is sufficient to return to normal hand and wrist function in all three fracture patterns. Both 50% and 75% union are unnecessary and increase the risk of post-fracture stiffness. This study has also demonstrated the feasibility of finite element analysis (FEA) in scaphoid waist fracture research. FEA is a sustainable method which does not require the use of finite scaphoid cadavers, hence increasing accessibility into future scaphoid waist fracture-related research.

Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

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.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10-20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Numerical analysis of the mechanical behaviour of intact and implanted lumbar functional spinal units: Effects of loading and boundary conditions

The objective of this study was to develop an improved finite element (FE) model of a lumbar functional spinal unit (FSU) and to subsequently analyse the deviations in load transfer owing to implantation. The effects of loading and boundary conditions on load transfer in intact and implanted FSUs and its relationship with the potential risk of vertebral fracture were investigated. The FE models of L1-L5 and L3-L4 FSUs, intact and implanted, were developed using patient-specific CT-scan dataset and segmentation of cortical and cancellous bone regions. The effect of submodelling technique, as compared to artificial boundary conditions, on the elastic behaviour of lumbar spine was examined. Applied forces and moments, corresponding to physiologic movements, were used as loading conditions. Results indicated that the loading and boundary conditions considerably affect stress-strain distributions within a FSU. This study, based on an improved FE model of a vertebra, highlights the importance of using the submodelling technique to adequately evaluate the mechanical behaviour of a FSU. In the intact FSU, strains of 200-400 µε were observed in the cancellous bone of vertebral body and pedicles. High equivalent stresses of 10-25 MPa and 1-5 MPa were generated around the pars interarticularis for cortical and cancellous regions, respectively. Implantation caused reductions of 85%-92% in the range of motion for all movements. Insertion of the intervertebral cage resulted in major deviations in load transfer across a FSU for all movements. The cancellous bone around cage experienced pronounced increase in stresses of 10-15 MPa, which indicated potential risk of failure initiation in the vertebra.

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms and assuming isotropic bone material property. The objective of the study is to develop an orthotropic bone remodelling algorithm for evaluation of peri-prosthetic bone adaptation in the uncemented implanted femur. The simulations considered loading conditions from a variety of daily activities. The orthotropic algorithm was tested on 2D and 3D models of the intact femur for verification of predicted results. The predicted orthotropic directionality, based on principal stress directions, was in agreement with the trabecular orientation in a micro-CT data of proximal femur. The validity of the proposed strain-based algorithm was assessed by comparing the predicted results of the orthotropic model with those of the strain-energy-density-based isotropic formulation. Despite agreement in cortical densities [Formula: see text], the isotropic remodelling algorithm tends to predict relatively higher values around the distal tip of the implant as compared to the orthotropic model. Both formulations predicted 4-8% bone resorption in the proximal femur. A linear regression analysis revealed a significant correlation [Formula: see text] between the stresses and strains on the cortex of the proximal femur, predicted by the isotropic and orthotropic formulations. Despite reasonable agreement in peri-prosthetic bone density distributions, the quantitative differences with isotropic model predictions highlight the combined influences of bone orthotropy and mechanical stimulus in the adaptation process.

A Contemporary View of the Diagnosis of Osteoporosis in Patients With Axial Spondyloarthritis

Axial spondyloarthritis (axSpA) is a chronic inflammatory disease that primarily affects the axial joints. Altered bone metabolism associated with chronic inflammation leads to both new bone formation in the spine and increased bone loss. It is known that patients with axSpA have a high prevalence of osteoporosis and fractures. However, there is no consensus on which imaging modality is the most appropriate for diagnosing osteoporosis in axSpA. Bone mineral density measurement using dual-energy X-ray absorptiometry is the primary diagnostic method for osteoporosis, but it has notable limitations in patients with axSpA. This method may lead to the overestimation of bone density in patients with axSpA because they often exhibit abnormal calcification of spinal ligaments or syndesmophytes. Therefore, the method may not provide adequate information about bone microarchitecture. These limitations result in the underdiagnosis of osteoporosis. Recently, new imaging techniques, such as high-resolution peripheral quantitative computed tomography, and trabecular bone score have been introduced for the evaluation of osteoporosis risk in patients with axSpA. In this review, we summarize the current knowledge regarding imaging techniques for diagnosing osteoporosis in patients with axSpA.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Multiscale design of artificial bones with biomimetic elastic microstructures

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

[General anatomy and image reconstruction analysis of the proximal femoral trabecular structures]

Objective

To investigate the three-dimensional structure of proximal femoral trabeculae, analyze the formation mechanism, and explore its relationship with the occurrence and treatment of proximal femoral fractures.

Methods

Six cadaver adult femur specimens were harvested and the gross specimens containing both trabecular system and cortical bone were established by hand scraping. All samples were scanned by micro-CT and the CT images were input into Mimics18.0 software to establish the digital proximal femoral model containing trabecular structure. The spatial distribution of trabecular system was observed, and the relations between trabecular bone and the proximal femur surface and related anatomical landmarks were analyzed in digital models.

Results

The gross specimen and digital models of trabecular system were successfully established. The trabecular system of proximal femur could be divided into two groups: the horizontal and vertical trabecular. The horizontal trabecular arose from the base of greater trochanter, gone along the direction of femoral neck, and terminated at the center of femoral head. The vertical trabecular began from the base of lesser trochanter and femoral calcar, gone radically upward, and reached the femoral head. The average distance of the horizontal trabecular to the greater trochanter was 22.66 mm (range, 17.3-26.8 mm). In the femoral head, the horizontal trabecula and the vertical trabecula were fused into a kind of sphere, and the distances from the horizontal trabecula to the surface of the femoral head vary in different sections. The average distance of trabecular ball to the femoral head surface was 6.88 mm (range, 6.3-7.2 mm) in sagittal plane, 6.32 mm (range, 5.8-7.6 mm) in coronal plane, and 6.30 mm (range, 5.6-6.3 mm) in cross section. The vertical and horizontal trabeculae intersect obliquely, and the average angle of horizontal trabecular and vertical one was 140.67° (range, 129-150°).

Conclusion

The trabecular system exhibits a unique spatial configuration, which is the main internal support of proximal femur. Restoration of the integrity of trabecular structure is the important goal of proximal femoral fractures.

Assessment of finite element models for prediction of osteoporotic fracture

With increasing life expectancy and mortality rates, the burden of osteoporotic hip fractures is continually on an upward trend. In terms of prevention, there are several osteoporosis treatment strategies such as anti-resorptive drug treatments, which attempt to retard the rate of bone resorption, while promoting the rate of formation. With respect to prediction, several studies have provided insights into obtaining bone strength by non-invasive means through the application of FE analysis. However, what valuable information can we obtain from FE studies that have focused on osteoporosis research, with respect to the prediction of osteoporotic fractures? This paper aims to fine studies that have used FE analysis to predict fractures in the proximal femur through a systematic search of literature using PUBMED, with the main objective of supporting the diagnosis of osteoporosis. The focus of these FE studies is first discussed, and the methodological aspects are summarized, by mainly comparing and contrasting their meshing properties, material properties, and boundary conditions. The implications of these methodological differences in FE modelling processes and propositions with the aim of consolidating or minimalizing these differences are further discussed. We proved that studies need to start converging in terms of their input parameters to make the FE method applicable to clinical settings. This, in turn, will decrease the time needed for in vitro tests. Current advancements in FE analysis need to be consolidated before any further steps can be taken to implement engineering analysis into the clinical scenario.

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.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone

BACKGROUND

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface.

METHODS

Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness.

FINDINGS

Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm³ density.

INTERPRETATION

In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.

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.

Estimation of Local Bone Loads for the Volume of Interest

Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

Spatial resolution and measurement uncertainty of strains in bone and bone-cement interface using digital volume correlation

The measurement uncertainty of strains has been assessed in a bone analogue (sawbone), bovine trabecular bone and bone-cement interface specimens under zero load using the Digital Volume Correlation (DVC) method. The effects of sub-volume size, sample constraint and preload on the measured strain uncertainty have been examined. There is generally a trade-off between the measurement uncertainty and the spatial resolution. Suitable sub-volume sizes have been be selected based on a compromise between the measurement uncertainty and the spatial resolution of the cases considered. A ratio of sub-volume size to a microstructure characteristic (Tb.Sp) was introduced to reflect a suitable spatial resolution, and the measurement uncertainty associated was assessed. Specifically, ratios between 1.6 and 4 appear to give rise to standard deviations in the measured strains between 166 and 620 με in all the cases considered, which would seem to suffice for strain analysis in pre as well as post yield loading regimes. A microscale finite element (μFE) model was built from the CT images of the sawbone, and the results from the μFE model and a continuum FE model were compared with those from the DVC. The strain results were found to differ significantly between the two methods at tissue level, consistent in trend with the results found in human bones, indicating mainly a limitation of the current DVC method in mapping strains at this level.

Cortical and trabecular load sharing in the human femoral neck

The relative role of the cortical vs trabecular bone in the load-carrying capacity of the proximal femur-a fundamental issue in both basic-science and clinical biomechanics-remains unclear. To gain insight into this issue, we performed micro-CT-based, linear elastic finite element analysis (61.5-micron-sized elements; ~280 million elements per model) on 18 proximal femurs (5M, 13F, ages 61-93 years) to quantify the fraction of frontal-plane bending moment shared by the cortical vs trabecular bone in the femoral neck, as well as the associated spatial distributions of stress. Analyses were performed separately for a sideways fall and stance loading. For both loading modes and across all 18 bones, we found consistent patterns of load-sharing in the neck: most proximally, the trabecular bone took most of the load; moving distally, the cortical bone took increasingly more of the load; and more distally, there was a region of uniform load-sharing, the cortical bone taking the majority of the load. This distal region of uniform load-sharing extended more for fall than stance loading (77 ± 8% vs 51 ± 6% of the neck length for fall vs. stance; mean ± SD) but the fraction of total load taken by the cortical bone in that region was greater for stance loading (88 ± 5% vs. 64 ± 9% for stance vs. fall). Locally, maximum stress levels occurred in the cortical bone distally, but in the trabecular bone proximally. Although the distal cortex showed qualitative stress distributions consistent with the behavior of an Euler-type beam, quantitatively beam theory did not apply. We conclude that consistent and well-delineated regions of uniform load-sharing and load-transfer between the cortical and trabecular bone exist within the femoral neck, the details of which depend on the external loading conditions.

Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption

Patient-specific analysis of bones is considered an important tool for diagnosis and treatment of skeletal diseases and for clinical research aimed at understanding the etiology of skeletal diseases and the effects of different types of treatment on their progress. In this article, we discuss how integration of several important components enables accurate and cost-effective patient-specific bone analysis, focusing primarily on patient-specific finite element (FE) modeling of bones. First, the different components are briefly reviewed. Then, two important aspects of patient-specific FE modeling, namely integration of modeling components and automation of modeling approaches, are discussed. We conclude with a section on validation of patient-specific modeling results, possible applications of patient-specific modeling procedures, current limitations of the modeling approaches, and possible areas for future research.

A multiscale analytical approach for bone remodeling simulations: linking scales from collagen to trabeculae

Bone is a dynamic and hierarchical porous material whose spatial and temporal mechanical properties can vary considerably due to differences in its microstructure and due to remodeling. Hence, a multiscale analytical approach, which combines bone structural information at multiple scales to the remodeling cellular activities, could form an efficient, accurate and beneficial framework for the prognosis of changes in bone properties due to, e.g., bone diseases. In this study, an analytical formulation of bone remodeling integrated with multiscale micromechanical models is proposed to investigate the effects of structural changes at the nanometer level (collagen scale) on those at higher levels (tissue scale). Specific goals of this study are to derive a mechanical stimulus sensed by the osteocytes using a multiscale framework, to test the accuracy of the multiscale model for the prediction of bone density, and to demonstrate its multiscale capabilities by predicting changes in bone density due to changes occurring at the molecular level. At each different level, the bone composition was modeled as a two-phase material which made it possible to: (1) find a closed-form solution for the energy-based mechanical stimulus sensed by the osteocytes and (2) describe the anisotropic elastic properties at higher levels as a function of the stiffness of the elementary components (collagen, hydroxyapatite and water) at lower levels. The accuracy of the proposed multiscale model of bone remodeling was tested first by comparing the analytical bone volume fraction predictions to those obtained from the corresponding μFE-based computational model. Differences between analytical and numerical predictions were less than 1% while the computational time was drastically reduced, namely by a factor of 1 million. In a further analysis, the effects of changes in collagen and hydroxyapatite volume fractions on the bone remodeling process were simulated, and it was found that such changes considerably affect the bone density at the millimeter scale. In fact, smaller tissue density induces remodeling activities leading to finally higher overall bone density. The multiscale analytical model proposed in this study potentially provides an accurate and efficient tool for simulating patient-specific bone remodeling, which might be of importance in particular for the hip and spine, where an accurate assessment of bone micro-architecture is not possible.

The paradox of Wolff's theories

The upper femur has long held a fascination for both clinicians and bioengineers as it contains two trabecular columns obviously related to its function. In this respect two theories as to the formation of these columns have developed, both associated with Wolff: the Trajectorial Theory, which relates mainly to the passage of forces through the cancellous bone of the upper femur, and Wolff's Law of bone formation, which describes the bone's reaction to these forces and relates to bone in general. The two concepts nevertheless are often used synonymously. The Trajectorial Theory propounds that these cancellous structures in the femoral neck are due to both tension and compression forces, while modern day concepts of Wolff's Law only acknowledge the action of compression forces: and herein lies the paradox. The Trajectorial Theory and Wolff's Law, when applied to the upper femur, are mutually exclusive. The evidence, anatomical and physiological, indicates that bone forms within the femoral neck solely under the influence of compression forces. This would indicate that the Trajectorial Theory is not appropriate for this region. An alternative conceptual way of looking at this region is presented which eliminates this theory and resolves the paradox.

Development of an Inertia-Driven Model of Sideways Fall for Detailed Study of Femur Fracture Mechanics

A new method for laboratory testing of human proximal femora in conditions simulating a sideways fall was developed. Additionally, in order to analyze the strain state in future cadaveric tests, digital image correlation (DIC) was validated as a tool for strain field measurement on the bone of the femoral neck. A fall simulator which included models for the body mass, combined lateral femur and pelvis mass, pelvis stiffness, and trochanteric soft tissue was designed. The characteristics of each element were derived and developed based on human data from the literature. The simulator was verified by loading a state-of-the-art surrogate femur and comparing the resulting force-time trace to published, human volunteer experiments. To validate the DIC, 20 human proximal femora were prepared with a strain rosette and speckle paint pattern, and loaded to 50% of their predicted failure load at a low compression rate. Strain rosettes were taken as the gold standard, and minimum principal strains from the DIC and the rosettes were compared using descriptive statistics. The initial slope of the force-time curve obtained in the fall simulator matched published human volunteer data, with local peaks superimposed in the model due to internal vibrations of the spring used to model the pelvis stiffness. Global force magnitude and temporal characteristics were within 2% of published volunteer experiments. The DIC minimum principal strains were found to be accurate to 127±239μɛ. These tools will allow more biofidelic laboratory simulation of falls to the side, and more detailed analysis of proximal femur failure mechanisms using human cadaver specimens.

Towards patient-specific material modeling of trabecular bone post-yield behavior

Bone diseases such as osteoporosis are one of the main causes of bone fracture and often result in hospitalization and long recovery periods. Researchers are aiming to develop new tools that consider the multiple determinants acting at the different scales of bone, and which can be used to clinically estimate patient-specific fracture risk and also assess the efficacy of new therapies. The main step towards this goal is a deep understanding of the bone organ, and is achieved by modeling the complexity of the structure and the high variability of the mechanical outcome. This review uses a hierarchical approach to evaluate bone mechanics at the macroscale, microscale, and nanoscale levels and the interactions between scales. The first section analyzes the experimental evidence of bone mechanics in the elastic and inelastic regions, microdamage generation, and post-yield toughening mechanisms from the organ level to the ultrastructural level. On the basis of these observations, the second section provides an overview of the constitutive models available to describe bone mechanics and predict patient-specific outcomes. Overall, the role of the hierarchical structure of bone and the interplay between each level is highlighted, and their effect is evaluated in terms of modeling biological variability and patient specificity.

Patient-specific finite element modeling of bones

Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.

Multi-scale finite element modelling at the posterior lumbar vertebra: analysis of pedicle stresses due to pars fracture

Multi-scale finite element (FE) model is a cost-effective way to analyse stress response of micro-level structures to the changes in loading at macro-level. This study deals with the development of a multi-scale model of a human vertebra and stress changes in the pedicle at high resolution after a gross fracture at the posterior neural arch. Spondylolysis (pars fracture) is a painful condition occurring in the vertebral neural arch and common especially among the athletic young population. The fracture of the pars significantly alters load distribution and load transfer characteristics at the neural arch. Structural changes in the posterior vertebra due to the new loading patterns can trigger secondary complications. Clinical reports have shown the association of pedicle hypertrophy or pedicle fracture with unilateral pars fractures. However, the biomechanical consequences of pars fracture and its effect on the pedicle have never been studied in detail. Therefore, we prepared a multi-scale model of posterior vertebra with continuum laminar complex model combined with micro-FE model of a pedicle section. The results showed that stress at the contralateral pars and pedicle increased after unilateral pars fracture simulation. High-stress regions were found around the outer boundaries of the pedicle. This model and information are helpful in understanding the stress changes in the pedicle and can be used for adaptive remodelling studies.

Experimental evaluation of new concepts in hip arthroplasty

In this thesis we evaluated two different hip arthroplasty concepts trough in vitro studies and numerical analyses. The cortical strains in the femoral neck area were increased by 10 to 15 % after insertion of a resurfacing femoral component compared to values of the intact femur, shown in an in vitro study on human cadaver femurs. There is an increased risk of femoral neck fracture after hip resurfacing arthroplasty. An increase of 10 to 15 % in femoral neck strains is limited, and cannot alone explain these fractures. Together with patient specific and surgical factors, however, increased strain can contribute to increased risk of fracture. An in vitro study showed that increasing the neck length in combination with retroversion or reduced neck shaft angle on a standard cementless femoral stem does not compromise the stability of the stem. The strain pattern in the proximal femur increased significantly at several measuring sites when the version and length of neck were altered. However, the changes were probably too small to have clinical relevance. In a validation study we have shown that a subject specific finite element analysis is able to perform reasonable predictions of strains and stress shielding after insertion of a femoral stem in human cadaver femurs. The usage of finite element models can be a valuable supplement to in vitro tests of femoral strain pattern around hip arthroplasty. Finally, a patient case shows that bone resorption around an implant caused by stress shielding can in extreme cases lead to periprosthetic fracture.

Effect of different irrigating solutions and endodontic sealers on bond strength of the dentin-post interface with and without defects

AIMS

To investigate how the interfacial shear strength of the dentin-post interface with and without defects changes for different combinations irrigant/sealer.

METHODS

In forty human decoronated and instrumented teeth, fibreglass posts were inserted. The obtained root segments were randomly assigned to four different groups according to the irrigant adopted and the cement used to seal the root canal. The root segments were processed for metyl-methacrylate embedding. Serial sections were obtained and submitted to histomorphometric analyses in order to observe any defect of adhesion at the dentin-post interface and to measure the defects' dimension. The serial sections were also submitted to micro-push-out test. The measured shear strength values were subjected to statistical analysis by one-way ANOVA. The values of bond strength determined for the defective samples were correlated with the dimension of the defects. Finite element models were built to interpret and corroborate the experimental findings.

RESULTS

ANOVA showed that the generic combination irrigant/sealer does not affect the interfacial shear strength values. The bond strength of the samples without defects was averagely twice as large as that of the defective samples. The defects occupying more than 12% of the total transverse section area of the endodontic cement layer led to a reduction of the bond strength of about 70%. The predictions of the finite element models were in agreement with the experimental results.

CONCLUSION

Defects occupying less than 2% of the total transverse section area of the cement layer were shown to be acceptable as they have rather negligible effects on the shear strength values. Technologies/protocols should be developed to minimize the number and the size of the defects.

Evolution of load transfer between hydroxyapatite and collagen during creep deformation of bone

While the matrix/reinforcement load-transfer occurring at the micro- and nanoscale in nonbiological composites subjected to creep deformation is well understood, this topic has been little studied in biological composites such as bone. Here, for the first time in bone, the mechanisms of time-dependent load transfer occurring at the nanoscale between the collagen phase and the hydroxyapatite (HAP) platelets are studied. Bovine cortical bone samples are subjected to synchrotron X-ray diffraction to measure in situ the evolution of elastic strains in the crystalline HAP phase and the evolution of viscoelastic strains accumulating in the mineralized collagen fibrils under creep conditions at body temperature. For a constant compressive stress, both types of strains increase linearly with time. This suggests that bone, as it deforms macroscopically, is behaving as a traditional composite, shedding load from the more compliant, viscoelastic collagen matrix to the reinforcing elastic HAP platelets. This behavior is modeled by finite-element simulation carried out at the fibrillar level.

Simulating Distal Radius Fracture Strength Using Biomechanical Tests: A Modeling Study Examining the Influence of Boundary Conditions

Distal radius fracture strength has been quantified using in vitro biomechanical testing. These tests are frequently performed using one of two methods: (1) load is applied directly to the embedded isolated radius or (2) load is applied through the hand with the wrist joint intact. Fracture loads established using the isolated radius method are consistently 1.5 to 3 times greater than those for the intact wrist method. To address this discrepancy, a validated finite element modeling procedure was used to predict distal radius fracture strength for 22 female forearms under boundary conditions simulating the isolated radius and intact wrist method. Predicted fracture strength was highly correlated between methods (r = 0.94; p < 0.001); however, intact wrist simulations were characterized by significantly reduced cortical shell load carriage and increased stress and strain concentrations. These changes resulted in fracture strength values less than half those predicted for the isolated radius simulations (2274 ± 824 N for isolated radius, 1124 ± 375 N for intact wrist; p < 0.001). The isolated radius method underestimated the mechanical importance of the trabecular compartment compared to the more physiologically relevant intact wrist scenario. These differences should be borne in mind when interpreting the physiologic importance of mechanical testing and simulation results.

Inter-sex differences in structural properties of aging femora: implications on differential bone fragility: a cadaver study

In this paper we examined age-related and sex-specific deterioration in bone strength of the proximal femur reflected in mechanical properties from dual energy X-ray absorptiometry (DXA)-based hip structural analysis (HSA) on a cadaveric sample from the Balkans. Cadaveric studies permit more precise measurement of HSA parameters and allow further analyses by micromorphometric methods. DXA and HSA analysis was performed on a total of 138 cadaveric proximal femora (63 female, 75 male, age range 20-101 years) from Belgrade. HSA parameters are reported for three standard regions of the proximal femur (narrow neck, intertrochanteric, and shaft). Major age-related findings include an increase in the radius of gyration (first reported in this study), a decline in the cross-sectional area (CSA), a shift in the centroid towards the medial cortex, higher buckling ratios and lower section moduli. Whereas age appears to affect mostly the neck region in men, weakening is also evident in the intertrochanteric region in women, particularly after the age of 80. Aging femoral neck declines in bending strength and increases in buckling susceptibility. The reduced bone mass tends to be distributed farther from the centroidal axis (increase in radius of gyration with decline in CSA). Bone mass is preferentially lost from the lateral part of the cross-section shifting the centroid towards the medial cortex which may increase fragility of the lateral part during fall impact. Results of this study contribute to the epidemiologic data on gender differences and age trends in aging male and female femora.