MicroCT-based finite element models as a tool for virtual testing of cortical bone

Finite element analysis of bone mechanical properties using MRI-derived bound and pore water concentration maps

Ultrashort echo time (UTE) MRI techniques can be used to image the concentration of water in bones. Particularly, quantitative MRI imaging of collagen-bound water concentration (Cbw) and pore water concentration (Cpw) in cortical bone have been shown as potential biomarkers for bone fracture risk. To investigate the effect of Cbw and Cpw on the evaluation of bone mechanical properties, MRI-based finite element models of cadaver radii were generated with tissue material properties derived from 3 D maps of Cbw and Cpw measurements. Three-point bending tests were simulated by means of the finite element method to predict bending properties of the bone and the results were compared with those from direct mechanical testing. The study results demonstrate that these MRI-derived measures of Cbw and Cpw improve the prediction of bone mechanical properties in cadaver radii and have the potential to be useful in assessing patient-specific bone fragility risk.

Effects of different preservation on the mechanical properties of cortical bone under quasi-static and dynamic compression

Introduction: Mechanical properties of biological tissue are important for numerical simulations. Preservative treatments are necessary for disinfection and long-term storage when conducting biomechanical experimentation on materials. However, few studies have been focused on the effect of preservation on the mechanical properties of bone in a wide strain rate. The purpose of this study was to evaluate the influence of formalin and dehydration on the intrinsic mechanical properties of cortical bone from quasi-static to dynamic compression. Methods: Cube specimens were prepared from pig femur and divided into three groups (fresh, formalin, and dehydration). All samples underwent static and dynamic compression at a strain rate from 10^-3 s^-1 to 10³ s^-1. The ultimate stress, ultimate strain, elastic modulus, and strain-rate sensitivity exponent were calculated. A one-way ANOVA test was performed to determine if the preservation method showed significant differences in mechanical properties under at different strain rates. The morphology of the macroscopic and microscopic structure of bones was observed. Results: The results show that ultimate stress and ultimate strain increased as the strain rate increased, while the elastic modulus decreased. Formalin fixation and dehydration did not affect elastic modulus significantly whereas significantly increased the ultimate strain and ultimate stress. The strain-rate sensitivity exponent was the highest in the fresh group, followed by the formalin group and dehydration group. Different fracture mechanisms were observed on the fractured surface, with fresh and preserved bone tending to fracture along the oblique direction, and dried bone tending to fracture along the axial direction. Discussion: In conclusion, preservation with both formalin and dehydration showed an influence on mechanical properties. The influence of the preservation method on material properties should be fully considered in developing a numerical simulation model, especially for high strain rate simulation.

Correlation of Bone Material Model Using Voxel Mesh and Parametric Optimization

The authors present an algorithm for determining the stiffness of the bone tissue for individual ranges of bone density. The paper begins with the preparation and appropriate mechanical processing of samples from the bovine femur and their imaging using computed tomography and then processing DICOM files in the MIMICS system. During the processing of DICOM files, particular emphasis was placed on defining basic planes along the sides of the samples, which improved the representation of sample geometry in the models. The MIMICS system transformed DICOM images into voxel models from which the whole bone FE model was built in the next step. A single voxel represents the averaged density of the real sample in a very small finite volume. In the numerical model, it is represented by the HEX8 element, which is a cube. All voxels were divided into groups that were assigned average equivalent densities. Then, the previously prepared samples were loaded to failure in a three-point bending test. The force waveforms as a function of the deflection of samples were obtained, based on which the global stiffness of the entire sample was determined. To determine the stiffness of each averaged voxel density value, the authors used advanced optimization analyses, during which numerical analyses were carried out simultaneously, independently mapping six experimental tests. Ultimately, the use of genetic algorithms made it possible to select a set of stiffness parameters for which the error of mapping the global stiffness for all samples was the smallest. The discrepancies obtained were less than 5%, which the authors considered satisfactory by the authors for such a heterogeneous medium and for samples collected from different parts of the bone. Finally, the determined data were validated for the sample that was not involved in the correlation of material parameters. The stiffness was 7% lower than in the experimental test.

Finite element modeling of multiple density materials of bone specimens for biomechanical behavior evaluation

The finite elements method allied with the computerized axial tomography (CT) is a mathematical modeling technique that allows constructing computational models for bone specimens from CT data. The objective of this work was to compare the experimental biomechanical behavior by three-point bending tests of porcine femur specimens with different types of computational models generated through the finite elements’ method and a multiple density materials assignation scheme. Using five femur specimens, 25 scenarios were created with differing quantities of materials. This latter was applied to computational models and in bone specimens subjected to failure. Among the three main highlights found, first, the results evidenced high precision in predicting experimental reaction force versus displacement in the models with larger number of assigned materials, with maximal results being an R2 of 0.99 and a minimum root-mean-square error of 3.29%. Secondly, measured and computed elastic stiffness values follow same trend with regard to specimen mass, and the latter underestimates stiffness values a 6% in average. Third and final highlight, this model can precisely and non-invasively assess bone tissue mechanical resistance based on subject-specific CT data, particularly if specimen deformation values at fracture are considered as part of the assessment procedure.

Is the 0.2%-Strain-Offset Approach Appropriate for Calculating the Yield Stress of Cortical Bone?

The 0.2% strain offset approach is mostly used to calculate the yield stress and serves as an efficient method for cross-lab comparisons of measured material properties. However, it is difficult to accurately determine the yield of the bone. Especially when computational models require accurate material parameters, clarification of the yield point is needed. We tested 24 cortical specimens harvested from six bovine femora in three-point bending mode, and 11 bovine femoral cortical specimens in the tensile mode. The Young's modulus and yield stress for each specimen derived from the specimen-specific finite element (FE) optimization method was regarded as the most ideal constitutive parameter. Then, the strain offset optimization method was used to find the strain offset closest to the ideal yield stress for the 24 specimens. The results showed that the 0 strain offsets underestimated (- 25%) the yield stress in bending and tensile tests, while the 0.2% strain offsets overestimated the yield stress (+ 65%) in three-point bending tests. Instead, the yield stress determined by 0.007 and 0.05% strain offset for bending and tensile loading respectively, can effectively characterize the biomechanical responses of the bone, thereby helping to build an accurate FE model.

Nondestructive Assessment of Growing Rat Tibial Mechanical Properties Under Three-Point Bending: A Microcomputed Tomography Based Finite Element Study

Microcomputed tomography (micro-CT) based finite element models (FEM) are efficient tools to assess bone mechanical properties. Although they have been developed for different animal models, there is still a lack of data for growing rat long bone models. This study aimed at developing and calibrating voxel-based FEMs using micro-CT scans and experimental data. Twenty-four tibiae were extracted from rats aged 28, 56, and 84 days old (d.o.) (n = 8/group), and their stiffness values were evaluated using three-point bending tests. Prior to testing, tibiae were scanned, reconstructed, and converted into FEM composed of heterogeneous bone properties based on pixel grayscales. Three element material laws (one per group) were calibrated using back-calculation process based on experimental bending data. Two additional specimens per group were used for model verification. The calibrated rigidity-density (E-ρ) relationships were different for each group: E28 = 10,320·ρash3.45; E56 = 43,620·ρash4.41; E84 = 20,090·ρash2.0. Obtained correlations between experimental and FEM stiffness values were 0.43, 0.10, and 0.66 with root-mean-square error (RMSE) of 14.4%, 17.4%, and 15.2% for 28, 56, and 84 d.o. groups, respectively. Prediction errors were less than 13.5% for 28 and 84 d.o. groups but reached 57.1% for the 56 d.o. group. Relationships between bone physical and mechanical properties were found to change during the growth, similarly to bending stiffness values, which increased with bone development. The reduced correlation observed for the 56 d.o. group may be related to the pubescent transition at that age group. These FE models will be useful for investigation of bone behavior in growing rats.

Multiscale finite element modeling of mechanical strains and fluid flow in osteocyte lacunocanalicular system

Osteocytes form over 90% of the bone cells and are postulated to be mechanosensors responsible for regulating the function of osteoclasts and osteoblasts in bone modeling and remodeling. Physical activity results in mechanical loading on the bones. Osteocytes are thought to be the main mechanosensory cells in bone. Upon load osteocytes secrete key factors initiating downstream signaling pathways that regulate skeletal metabolism including the Wnt/β-catenin signaling pathway. Osteocytes have dendritic structures and are housed in the lacunae and canaliculi within the bone matrix. Mechanical loading is known to have two primary effects, namely a mechanical strain (membrane disruption by stretching) on the lacunae/cells, and fluid flow, in the form of fluid flow shear stress (FFSS), in the space between the cell membranes and the lacuna-canalicular walls. In response, osteocytes get activated via a process called mechanotransduction in which mechanical signals are transduced to biological responses. The study of mechanotransduction is a complex subject involving principles of engineering mechanics as well as biological signaling pathway studies. Several length scales are involved as the mechanical loading on macro sized bones are converted to strain and FFSS responses at the micro-cellular level. Experimental measurements of strain and FFSS at the cellular level are very difficult and correlating them to specific biological activity makes this a very challenging task. One of the methods commonly adopted is a multi-scale approach that combines biological and mechanical experimentation with in silico numerical modeling of the engineering aspects of the problem. Finite element analysis along with fluid-structure interaction methodologies are used to compute the mechanical strain and FFSS. These types of analyses often involve a multi-length scale approach where models of both the macro bone structure and micro structure at the cellular length scale are used. Imaging modalities play a crucial role in the development of the models and present their own challenges. This paper reviews the efforts of various research groups in addressing this problem and presents the work in our research group. A clear understanding of how mechanical stimuli affect the lacunae and perilacunar tissue strains and shear stresses on the cellular membranes may ultimately lead to a better understanding of the process of osteocyte activation.

Finite element analysis of bone strength in osteogenesis imperfecta

As a dedicated experimentalist, John Currey praised the high potential of finite element (FE) analysis but also recognized its critical limitations. The application of the FE methodology to bone tissue is reviewed in the light of his enthusiastic and colorful statements. In the past decades, FE analysis contributed substantially to the understanding of structure-function properties in the hierarchical organization of bone and to the simulation of bone adaptation. The systematic experimental validation of FE analysis of bone strength in anatomical locations at risk of fracture led to its application in clinical studies to evaluate efficacy of antiresorptive or anabolic treatment of bone fragility. Beyond the successful analyses of healthy or osteoporotic bone, FE analysis becomes increasingly involved in the investigation of other fragility-related bone diseases. The case of osteogenesis imperfecta (OI) is exposed, the multiscale alterations of the bone tissue and the effect of treatment summarized. A few FE analyses attempting to answer open questions in OI are then reported. An original study is finally presented that explored the structural properties of the Brtl/+ murine model of OI type IV subjected to sclerostin neutralizing antibody treatment using microFE analysis. The use of identical material properties in the four-point bending FE simulations of the femora reproduced not only the experimental values but also the statistical comparisons examining the effect of disease and treatment. Further efforts are needed to build upon the extraordinary legacy of John Currey and clarify the impact of different bone diseases on the hierarchical mechanical properties of bone.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

Optimizing Accuracy of Proximal Femur Elastic Modulus Equations

Quantitative computed tomography-based finite element analysis (QCT/FEA) is a promising tool to predict femoral properties. One of the modeling parameters required as input for QCT/FEA is the elastic modulus, which varies with the location-dependent bone mineral density (ash density). The aim of this study was to develop optimized equations for the femoral elastic modulus. An inverse QCT/FEA method was employed, using an optimization process to minimize the error between the predicted femoral stiffness values and experimental values. We determined optimal coefficients of an elastic modulus equation that was a function of ash density only, and also optimal coefficients for several other equations that included along with ash density combinations of the variables sex and age. All of the optimized models were found to be more accurate than models from the literature. It was found that the addition of the variables sex and age to ash density made very minor improvements in stiffness predictions compared to the model with ash density alone. Even though the addition of age did not remarkably improve the statistical metrics, the effect of age was reflected in the elastic modulus equations as a decline of about 9% over a 60-year interval.

The effect of storage time in saline solution on the material properties of cortical bone tissue

BACKGROUND

The use of saline in preserving bone specimens may affect the mechanical properties of specimens. Yet, the reported effects varied and contradicted to each other, with a lack of investigating constitutive material parameters. Therefore, we quantified the effects of preservation time on the constitutive properties of cortical bone.

METHODS

We collected 120 specimens from the mid-diaphysis of six male bovine femora, which were assigned to five groups, including fresh-frozen for 60 days (-20 °C), storage in saline for 3, 10, 36 and 60 days (25 °C). All specimens underwent quasi-static three-point bending tests with a loading rate of 0.02 mm/s. Using the optimization method combined with specimen-specific finite element models, the Young's modulus, tangent modulus, yield stress, effective plastic strain, yield strain, ultimate stress, and toughness were calculated.

FINDINGS

Saline preservation resulted in a significant decrease of Young's modulus, yield stress, ultimate stress and pre-yield toughness (P < 0.001), and a significant increase of effective plastic strain (P = 0.034). After 10 days of preservation, yield stress and pre-yield toughness decreased -14.9% and -21.4%, respectively, and they continued to decrease with longer preservation time. After 36 days of preservation, Young's modulus and ultimate stress decreased -19.2% and -17.3%, respectively, and continued to decrease with longer preservation time. Our data also showed changes of material properties collected after 3-day saline preservation, while the low statistical power must be considered for this group.

INTERPRETATION

Saline preservation impacts on mechanical properties of cortical bone tissue and the effect is already observable after 3 days.

Combining specimen-specific finite-element models and optimization in cortical-bone material characterization improves prediction accuracy in three-point bending tests

Although the beam theory is widely used for calculating material parameters in three-point bending test, it cannot accurately describe the biomechanical properties of specimens after the yield. Hence, we propose a finite element (FE) based optimization method to obtain accurate bone material parameters from three-point bending test. We tested 80 machined bovine cortical bone specimens at both longitudinal and transverse directions using three-point bending. We then adopted the beam theory and the FE-based optimization method combined with specimen-specific FE models to derive the material parameters of cortical bone. We compared data obtained using these two methods and further evaluated two groups of parameters with three-point bending simulations. Our data indicated that the FE models with material properties from the FE-based optimization method showed best agreements with experimental data for the entire force-displacement responses, including the post-yield region. Using the beam theory, the yield stresses derived from 0.0058% strain offset for the longitudinal specimen and 0.0052% strain offset for the transverse specimen are closer to those derived from the FE-based optimization method, compared to yield stresses calculated without strain offset. In brief, we conclude that the optimization FE method is more appropriate than the traditional beam theory in identifying the material parameters of cortical bone for improving prediction accuracy in three-point bending mode. Given that the beam theory remains as a popular method because of its efficiency, we further provided correction functions to adjust parameters calculated from the beam theory for accurate FE simulation.