Finite element dependence of stress evaluation for human trabecular bone

Elastic response of trabecular bone under compression calculated using the firm and floppy boundary lattice element method

Micro-Finite Element analysis (μFEA) has become widely used in biomechanical research as a reliable tool for the prediction of bone mechanical properties within its microstructure such as apparent elastic modulus and strength. However, this method requires substantial computational resources and processing time. Here, we propose a computationally efficient alternative to FEA that can provide an accurate estimation of bone trabecular mechanical properties in a fast and quantitative way. A lattice element method (LEM) framework based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) open-source software package is employed to calculate the elastic response of trabecular bone cores. A novel procedure to handle pore-material boundaries is presented, referred to as the Firm and Floppy Boundary LEM (FFB-LEM). Our FFB-LEM calculations are compared to voxel- and geometry-based FEA benchmarks incorporating bovine and human trabecular bone cores imaged by micro Computed Tomography (μCT). Using 14 computer cores, the apparent elastic modulus calculation of a trabecular bone core from a μCT-based input with FFB-LEM required about 15 min, including conversion of the μCT data into a LAMMPS input file. In contrast, the FEA calculations on the same system including the mesh generation, required approximately 30 and 50 min for voxel- and geometry-based FEA, respectively. There were no statistically significant differences between FFB-LEM and voxel- or geometry-based FEA apparent elastic moduli (+24.3% or +7.41%, and +0.630% or -5.29% differences for bovine and human samples, respectively).

Experimental DVC validation of heterogeneous micro finite element models applied to subchondral trabecular bone of the humeral head

Subchondral trabecular bone (STB) undergoes adaptive changes during osteoarthritic (OA) disease progression. These changes alter both the mineralization patterns and structure of bone and may contribute to variations in the mechanical properties. Similarly, when images are downsampled - as is often performed in micro finite element model (microFEM) generation - the morphological and mineralization patterns may further alter the mechanical properties due to partial volume effects. MicroFEMs accounting for material heterogeneity can account for these tissue variations, but no studies have validated these with robust full-field testing methods. As such, this study compared homogeneous and heterogeneous microFEMs to experimentally loaded trabecular bone cores from the humeral head combined with digital volume correlation (DVC). These microFEMs were used to compare apparent mechanical properties between normal and OA STB. Morphological and mineralization patterns between groups were also compared. There were no significant differences in tissue or bone mineral density between groups. The only significant differences in morphometric parameters were in trabecular thickness between groups. There were no significant differences in linear regression parameters between normal and OA STB apparent mechanical properties estimated using heterogeneous microFEMs with an element-wise bilinear elastic-plastic constitutive model. Clinical significance: Validated heterogeneous microFEMs applied to STB of the humeral head have the potential to significantly improve our understanding of mechanical variations in the bone that occur during OA progression.

The Effect of Material Heterogeneity, Element Type, and Down-Sampling on Trabecular Stiffness in Micro Finite Element Models

Preclinical and clinical bone strength predictions can be elucidated by understanding bone mechanics at a variety of hierarchical levels. As such, down-sampled micro-CT images are often used to make comparisons across image resolutions or used to reduce computational resources in micro finite element models (µFEMs). Therefore, the objectives of this study were to compare trabecular apparent modulus among (i) hexahedral and tetrahedral µFEMs, (ii) µFEMs generated from 32, 64, and 64 µm down-sampled from 32 µm µCT scans, and (iii) µFEMs with homogeneous and heterogeneous tissue moduli. Trabecular µFEMs were generated from scans at the three spatial resolutions taken from the glenoid vault of 14 cadaveric specimens. Simulated unconstrained compression was performed and used to calculate and compare the apparent modulus of each µFEM. It was found that models derived from high-resolution images that account for material heterogeneity are nearly equivalent whether hexahedral or tetrahedral elements are used. However, translation of stiffness from down-sampled scans are not equivalent to scans performed at the down-sampled resolution, or that account for trabecular material heterogeneity. Material heterogeneity is most representative of in vivo trabecular bone and to accurately model trabecular mechanical properties, material heterogeneity should be considered in future µFEM development.

Influence of the shape of the micro-finite element model on the mechanical properties calculated from micro-finite element analysis

Assessing the biomechanical properties of trabecular bone is of major biological and clinical significance for the research of bone diseases, fractures and their treatments. Micro-finite element (µFE) models are becoming increasingly popular for investigating the biomechanical properties of trabecular bone. The shapes of µFE models typically include cube and cylinder. Whether there are differences between cubic and cylindrical µFE models has not yet been studied. In the present study, cubic and cylindrical µFE models of human vertebral trabecular bone were constructed. A 1% strain was prescribed to the model along the superior-inferior direction. E values were calculated from these models, and paired t-tests were performed to determine whether these were any differences between E values obtained from cubic and cylindrical models. The results demonstrated that there were no statistically significant differences in the E values between cubic and cylindrical models, and there were no significant differences in Von Mises stress distributions between the two models. These findings indicated that, to construct µFE models of vertebral trabecular bone, cubic or cylindrical models were both feasible. Choosing between the cubic or cylindrical µFE model is dependent upon the specific study design.

Use of micro-computed tomography for the assessment of periapical lesions in small rodents: a systematic review

This systematic review aimed to evaluate the literature on the acquisition-, reconstruction- and analysis parameters of micro-computed tomography (micro-CT) for the assessment of periapical lesions in rats and mice, and to illustrate the effect of variation in these parameters. The PubMed database was searched from 2000 to January 2015 (English-language publications) for reports on the use of micro-CT to evaluate periapical lesions in rats and mice. QUADAS criteria were used to rate the quality of the studies. To illustrate the effect of variations in acquisition-, reconstruction-, and analysis parameters on images of periapical lesions, micro-CT examination of two hemi-mandibles of mice, with periapical lesions around the first molar was undertaken. Twenty-one studies were identified, which analysed periapical lesions in rats or mice using micro-CT. According to the QUADAS, no study was classified as high-, seven were classified as moderate-, and 14 as low quality. The effect of variation in parameters was that voxel size may interfere with image sharpness, reconstruction may interfere with image sharpness and contrast, and inadequate plane orientation may alter the size of the periapical lesion. Nonpersonalized ROIs resulted in areas that were not part of the periapical lesion. Changing the limits of the threshold for bone-tissue visualization increased lesion size. There is no defined protocol for acquiring and analysing micro-CT images of periapical lesions in rats and mice. Furthermore, acquisition-, reconstruction- and analysis parameters are not adequately explained, which may compromise the scientific impact of the studies.

Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis

Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E.

Weakening mechanisms of the serpulid tube in a high-CO2 world

Many benthic marine organisms produce calcium carbonate (CaCO3) structures for mechanical protection through a biologically controlled calcification process. However, the oceans are becoming unfavorable for calcification because of the stress associated with ocean acidification (OA) and associated chemical changes such as declining saturation state of CaCO3 and decreasing seawater pH. This work studies the impacts of OA-driven decreased pH on the calcareous tubes produced by the serpulid tubeworm Hydroides elegans. Tubes grown under control and OA experimental conditions were measured for structural and mechanical properties, and their mechanical properties were further interpreted using finite element analysis (FEA). The near-future predicted pH value of 7.8 altered tube ultrastructure, volume, and density and decreased the mean tube hardness and elasticity by ∼ 80 and ∼ 70%, respectively. The crushing force required for breaking the tube was reduced by 64%. The FEA results demonstrated how a simulated predator attack may affect the structure with different structural and mechanical properties and consequently shift the stress development and distribution in the tubes, causing a more concentrated stress distribution and therefore leading to a lower ability to withstand attacks.

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.