Large-scale finite element analysis of human cancellous bone tissue micro computer tomography data: a convergence study

Computationally efficient dominant load-based local bone microstructure reconstruction method using topology optimization

The bone microstructure of the human proximal femur is clinically crucial for diagnosing skeletal pathologies, such as osteoporosis and bone metastases. The topology optimization-based bone microstructure method obtains these bone microstructures by converting low-resolution (LR) images into high-resolution images. However, this method is inherently computationally inefficient as it requires numerous finite elements, iterative analyses, and parallel computations. Therefore, this study proposes a novel topology optimization-based localised bone microstructure reconstruction method using the dominant load, which highly affects the selected region of interest (ROI), for efficient resolution enhancement. The load dependency of selected ROIs is quantified with a load dependency score. Then, the localised finite element model is constructed based on the local load estimation. Finally, the selected dominant load is applied as an input for the topology optimization-based bone microstructure reconstruction method. The reconstructed bone microstructure was similar to that of the conventional method. The localised finite element model applied by the dominant load effectively and accurately reconstructed the bone morphology and exhibited high computational efficiency. In conclusion, the dominant load-based approach can be used to construct a reasonable trabecular bone structure for ROI with high computational efficiency. The predictive performance of the proposed method was validated and showed promise for accurate trabecular bone structure prediction without additional radiation exposure.

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 Effects of the Porous Structure of Gyroid and Voronoi Hip Implants: A Finite Element Analysis Using an Experimentally Validated Model

Total hip arthroplasty (THA) is most likely one of the most successful surgical procedures in medicine. It is estimated that three in four patients live beyond the first post-operative year, so appropriate surgery is needed to alleviate an otherwise long-standing suboptimal functional level. However, research has shown that during a complete THA procedure, a solid hip implant inserted in the femur can damage the main arterial supply of the cortex and damage the medullary space, leading to cortical bone resorption. Therefore, this study aimed to design a porous hip implant with a focus on providing more space for better osteointegration, improving the medullary revascularisation and blood circulation of patients. Based on a review of the literature, a lightweight implant design was developed by applying topology optimisation and changing the materials of the implant. Gyroid and Voronoi lattice structures and a solid hip implant (as a control) were designed. In total, three designs of hip implants were constructed by using SolidWorks and nTopology software version 2.31. Point loads were applied at the x, y and z-axis to imitate the stance phase condition. The forces represented were x = 320 N, y = -170 N, and z = -2850 N. The materials that were used in this study were titanium alloys. All of the designs were then simulated by using Marc Mentat software version 2020 (MSC Software Corporation, Munich, Germany) via a finite element method. Analysis of the study on topology optimisation demonstrated that the Voronoi lattice structure yielded the lowest von Mises stress and displacement values, at 313.96 MPa and 1.50 mm, respectively, with titanium alloys as the materials. The results also indicate that porous hip implants have the potential to be implemented for hip implant replacement, whereby the mechanical integrity is still preserved. This result will not only help orthopaedic surgeons to justify the design choices, but could also provide new insights for future studies in biomechanics.

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.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53-0.65, average error of 13-17%). A lower correlation was found for failure load (R2 = 0.21-0.48, average error of 9-15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75-0.80 for stiffness, R2 = 0.55-0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Remodelling of trabecular bone in human distal tibia: A model based on an in-vivo HR-pQCT study

An abnormal remodelling process of bones can lead to various bone disorders, such as osteoporosis, making them prone to fracture. Simulations of load-induced remodelling of trabecular bone were used to investigate its response to mechanical signal. However, the role of mechanostat in trabecular-bone remodelling has not yet been investigated in simulations underpinned by a longitudinal in-vivo study in humans. In this work, a finite-element model based on a 6-month longitudinal in-vivo HR-pQCT study was developed and validated to investigate the effect of mechanical stimuli on bone remodelling. The simulated changes in microstructural parameters and density of trabecular bone were compared with respective experimental results. A maximum principal strain (MPS) and a maximum principal strain gradient (∇MPS) were used as mechanical signals to drive a five-stage mechanostat remodelling model, including additional over-strain and damage stages. It was found that the density distribution varied with the studied mechanical signals, along with decreasing with time levels of bone volume fraction BV/TV, trabecular thickness Tb.Th and bone surface area Tb.BS as well as increased trabecular separation Tb.Sp. Among these parameters, BV/TV and Tb.Th together with the bone-remodelling parameters from the MPS model demonstrated a significant correlation with the experimental data. The developed model provides a good foundation for further development and investigation of the relationships between mechanical loading and human-bone microarchitecture.

Characterising variability and regional correlations of microstructure and mechanical competence of human tibial trabecular bone: An in-vivo HR-pQCT study

OBJECTIVE

Quantifying spatial distribution of trabecular bone mechanical competence and microstructure is important for early diagnosis of skeletal disorders and potential risk of fracture. The objective of this study was to determine a spatial distribution of trabecular mechanical and morphological properties in human distal tibia and examine the contribution of regional variability of trabecular microarchitecture to mechanical competence.

METHODS

A total of 340 representative volume elements at five anatomic regions of trabecular bone - anterior, posterior, lateral, medial and centre - from ten white European-origin postmenopausal women were studied. Region-specific trabecular parameters such as trabecular volume fraction, trabecular thickness, trabecular number, trabecular surface area, trabecular separation, plate-like structure fraction and finite element analysis of trabecular stiffness were determined based on in-vivo high resolution peripheral quantitative computed tomographic (HR-pQCT) images of distal tibiae from ten postmenopausal women. Mean values were compared using analysis of variance. The correlations between morphological parameters and stiffness were calculated.

RESULTS

Significant regional variation in trabecular microarchitecture of the human distal tibia was observed (p < 0.05), with up to 106% differences between lowest (central and anterior) and highest (medial and posterior) regions. Higher proportion of plate-like trabecular morphology (63% and 53%) was found in medial and posterior regions in the distal tibia. Stiffness estimated from finite element models also differed significantly (p < 0.05), with stiffness being 4.5 times higher in the highest (medial) than lowest (central) regions. The bone volume fraction was the strongest correlate of stiffness in all regions.

CONCLUSION

A novel finding of this study is the fact that significant regional variation of stiffness derived from two-phased FEA model with individual trabecula representation correlated highly to regional morphology obtained from in-vivo HR-pQCT images at the distal tibia. The correlations between regional morphological parameters and mechanical competence of trabecular bone were consistent at all regions studied, with regional BV/TV showing the highest correlation. The method developed for regional analysis of trabecular mechanical competence may offer a better insight into the relationship between mechanical behaviour and microstructure of bone. The findings provide evidence needed to further justify a larger-cohort feasibility study for early detection of bone degenerative diseases: examining regional variations in mechanical competence and trabecular specifications may allow better understanding of fracture risks in addition to others contributing factors.

EVALUATING THE THEORY OF BONE MECHANOREGULATION IN THE PHYSIOLOGICAL LOADING SCENARIO

In this paper, the theory of bone mechanoregulation under physiological loading was evaluated. The entire right tibiae of wild type (WT, [Formula: see text]) and parathyroid hormone (PTH, [Formula: see text]) treated C57BL/6J female mice were scanned using an in vivo [Formula: see text]CT imaging system at 14, 16, 17, 18, 19, 20, 21, and 22 weeks. The PTH intervention started from week 18 until week 22. Subject-specific finite element (FE) models were created from the [Formula: see text]CT images and physiological loading condition was defined in the FE models. The rates of changes in bone mineral content (BMC), bone mineral density (BMD), and bone tissue density (TMD) were quantified over 40 anatomical compartments across the entire mouse tibia. The resulting values were then correlated to the average 1st principal tensile strain ([Formula: see text]) and the strain energy density (SED) for every compartment at weeks 18, 20, and 22. It was found that: in both groups, [Formula: see text] had a minimal effect on the variability of [Formula: see text]BMC ([Formula: see text]); SED had a significant effect on the variability of [Formula: see text]BMC only in the WT group ([Formula: see text]); [Formula: see text] had a significant effect on the variability of [Formula: see text]BMD only in the PTH group ([Formula: see text]); SED had a significant effect on the variability of [Formula: see text]BMD in both groups ([Formula: see text]); neither SED nor [Formula: see text] had a significant effect on the variability of [Formula: see text]TMD ([Formula: see text]). These results are the first to reveal the mechanism of bone mechanoregulation in the physiological loading scenario.

Micro Finite Element models of the vertebral body: Validation of local displacement predictions

The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R² = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.

Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: A validation study

Non-destructive 3D micro-computed tomography (microCT) based finite element (microFE) models are used to estimate bone mechanical properties at tissue level. However, their validation remains challenging. Recent improvements in the quantification of displacements in bone tissue biopsies subjected to staged compression, using refined Digital Volume Correlation (DVC) techniques, now provide a full field displacement information accurate enough to be used for microFE validation. In this study, three specimens (two humans and one bovine) were tested with two different experimental set-ups, and the resulting data processed with the same DVC algorithm. The resulting displacement vector field was compared to that predicted by microFE models solved with three different boundary conditions (BC): nominal force resultant, nominal displacement resultant, distributed displacement. The first two conditions were obtained directly from the measurements provided by the experimental jigs, whereas in the third case the displacement field measured by the DVC in the top and bottom layer of the specimen was applied. Results show excellent relationship between the numerical predictions (x) and the experiments (y) when using BC derived from the DVC measurements (U_X: y=1.07x-0.002, RMSE: 0.001mm; U_Y: y=1.03x-0.001, RMSE: 0.001mm; U_Z: y=x+0.0002, RMSE: 0.001 mm for bovine specimen), whereas only poor correlation was found using BCs according to experiment set-ups. In conclusion, microFE models were found to predict accurately the vectorial displacement field using interpolated displacement boundary condition from DVC measurement.