Virtual trabecular bone models and their mechanical response

Abstract

The study of the mechanical behaviour of trabecular bone has extensively employed micro-level finite element (microFE) models generated from images of real bone samples. It is now recognized that the key determinants of the mechanical behaviour of bone are related to its micro-architecture. The key indices of micro-architecture, in turn, depend on factors such as age, anatomical site, sex, and degree of osteoporosis. In practice, it is difficult to acquire sufficient samples that encompass these variations. In this preliminary study, a method of generating virtual finite element (FE) samples of trabecular bone is considered. Virtual samples, calibrated to satisfy some of the key micro-architectural characteristics, are generated computationally. The apparent level elastic and post-elastic mechanical behaviour of the generated samples is examined: the elastic mechanical response of these samples is found to compare well with natural trabecular bone studies conducted by previous investigators; the post-elastic response of virtual samples shows that material non-linearities have a much greater effect in comparison with geometrical non-linearity for the bone densities considered. Similar behaviour has been reported by previous studies conducted on real trabecular bone. It is concluded that virtual modelling presents a potentially valuable tool in the study of the mechanical behaviour of trabecular bone and the role of its micro-architecture.

Algorithms for a strain‐based plasticity criterion for bone

“…Several stress-based criteria have been considered for bone. These range from the extensively used isotropic von Mises criterion to the anisotropic Tsai-Wu [1] criterion [2][3][4][5][6][7][8][9][10][11]. Although some of the simpler isotropic criteria, perhaps employed because they were readily available, have been shown to be unsuitable for bone [3,8], other anisotropic ones require too many parameters, and their accuracy is not sufficient to justify the additional experimental effort required for the determination of the parameters [3,12].…”

Idealization through interactive modeling and experimental assessment of 3D-printed gyroid for trabecular bone scaffold

“…These significant works include the Gibson-Ashby model, Kelvin's tetrakaidecahedron model, beam-skeletons network, and Voronoi tessellations to name a few. [8][9][10] These models were chosen on the basis that they mimic the native bone morphologically and the deformation modes under loading.…”

Modeling microdamage behavior of cortical bone

“…Computational tools to model the mechanical behavior of bone at different length scales are mostly based on finite element (FE) analysis (Ruffoni and van Lenthe 2010). Specifically, considering the complex structure of bone, detailed microstructural FE (micro-FE) models have been developed to represent whole bones including the intricate geometries of both the trabecular network and the cortical compartment (Eswaran et al 2006;Donaldson et al 2008Donaldson et al , 2011Ruffoni et al 2012Ruffoni et al , 2013. Micro-FE models are often based on voxel meshes where image voxels (e.g., from micro-CT scans) are directly converted into hexahedral elements of identical shape and size.…”

“…Failure is typically modeled in micro-FE by changing the material properties of the bone elements according to a failure/yield criterion. This change in material properties has been based on plasticity (Donaldson et al 2008;Verhulp et al 2008a;Pankaj and Donaldson 2013) and nonlinear elasticity (Niebur et al 2000). However, the intrinsic material properties of bone depend on the complex organization of its basic constituents, namely a collagenous matrix with embedded platelike mineral crystals (Jager and Fratzl 2000).…”