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Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Purpose: The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods: Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5µm were performed and the indentation modulus was computed for each measurement. Results: The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8GPa, compared to the circumferential one, 12.3±3.5GPa, and radial one, 8.3±3.1GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9GPa, and along the lateral, 12.0±3.0GPa, directions) and the trabecular bone (Ei= 13.7±3.4GPa along the axial direction versus Ei=10.9±3.7GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3GPa). Conclusions: The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis. [ABSTRACT FROM AUTHOR]

Abstract: Osteoporosis related vertebral fractures are an increasing clinical problem in ageing societies. The prediction of vertebral fracture load from QCT-based anatomy-specific finite element simulations could be very useful in the management of patients with osteoporosis, especially with regard to a possible fracture prevention or treatment optimisation. A key property in finite element analysis is the yield surface for the trabecular bone material. This study is aimed at identifying continuum-level yield criteria for vertebral trabecular bone using micro-finite element models subjected to uni-axial, shear, and tri-axial loading. A fabric-dependent, orthotropic Tsai–Wu yield criterion is proposed in both stress and strain spaces. Nonlinear micro-finite element models of cubic vertebral trabecular bone samples with 5.62mm edge length were generated from . Kinematic boundary conditions were imposed and the specimen was loaded force controlled beyond yield in 17 different load cases (six uni-axial, three shear and eight multi-axial). The proposed yield criteria were fitted to the resulting yield data. Yield strains on-axis were significantly lower (10% in tension and 6% in compression) than in the transverse directions. Average yield strains were 0.7% in tension, 1.1% in compression, 1.0% in shear and ranged from 0.6% to 1.1% under multi-axial loading. In axial direction, maximum yield stress was 2.6MPa in tension and 4.7MPa in compression. Lowest shear stress was found in the transverse plane with 1.3MPa. Multi-axial yield stresses ranged between values for uni-axial tension and compression. Yield stresses depended significantly and substantially on both volume fraction and fabric. Yield strains depended also significantly on both bone volume fraction and fabric, but only weakly on the former. The standard error of the estimate and the concordance correlation coefficient of the yield surface were 5.47% and 0.93 in strain space and 13.58% and 0.96 in stress space. The results of this study are not only consistent with experimental data from the literature but also extend the current knowledge of yield to multi-axial load cases that can hardly be realised in a biomechanical experiment. The presented yield data and criteria will help improving the prediction of vertebral ultimate load using anatomy-specific finite element models. [Copyright &y& Elsevier]

Abstract: Vertebral fractures represent a major health problem and involve the progressive collapse of trabecular bone over large compressive strains. This collapse is driven by local failure and interaction of the trabecular rod and plate elements, which translates into stress softening and densification at the material level. Current constitutive models for trabecular bone are essentially limited to infinitesimal strains. Accordingly, the aim of this work was to extend our current phenomenological model of trabecular bone (Garcia et al., 2009) for the simulation of large compressive strains by including post-yield softening and densification. A constitutive model of trabecular bone based on both volume fraction and trabecular orientation was formulated in a proper theoretical framework, implemented in commercial FE software and validated with human vertebral sections subjected to large compressive strains. As it is for infinitesimal strains, the evolution of plastic strains and damage is described by local internal variables. An isotropic softening rule was controlled by the cumulated plastic strain and a non-linear elastic spring was added to account for densification of the porous material in moderate-to-large compressive strains beyond a given threshold. To avoid convergence problems occurring as a result of softening, a consistent visco-plastic regularization approach was adopted. The experimental results for 37 vertebral sections from previous work (Dall''Ara et al., 2010) were used to validate the constitutive model for compressive loading up to 45% of the average axial deformation. This validation study showed that the model provides both qualitative predictions of damage localization on the cortex and quantitative predictions of dissipated energy () of vertebral body behavior under large compressive strains. Since the evolution of the internal variables was considered in local manner, a mesh sensitivity analysis of the finite element model was conducted via two different mesh sizes and revealed that strain localization was dominated by trabecular bone heterogeneity. To our knowledge, this model is the first to simulate collapse of trabecular bone and may help improve the biomechanical understanding of several musculoskeletal conditions such as vertebral fractures or orthopedic implant migration. [Copyright &y& Elsevier]