Characterization of synthetic foam structures used to manufacture artificial vertebral trabecular bone.

Artificial materials reflecting the mechanical properties of human bone are essential for valid and reliable implant testing and design. They also are of great benefit for realistic simulation of surgical procedures. The objective of this study was therefore to characterize two groups of self-developed synthetic foam structures by static compressive testing and by microcomputed tomography. Two mineral fillers and varying amounts of a blowing agent were used to create different expansion behavior of the synthetic open-cell foams. The resulting compressive and morphometric properties thus differed within and also slightly between both groups. Apart from the structural anisotropy, the compressive and morphometric properties of the synthetic foam materials were shown to mirror the respective characteristics of human vertebral trabecular bone in good approximation. In conclusion, the artificial materials created can be used to manufacture valid synthetic bones for surgical training. Further, they provide novel possibilities for studying the relationship between trabecular bone microstructure and biomechanical properties.

A new multiscale micromechanical model of vertebral trabecular bones.

A new three-dimensional (3D) multiscale micromechanical model has been suggested as adept at predicting the overall linear anisotropic mechanical properties of a vertebral trabecular bone (VTB) highly porous microstructure. A nested 3D modeling analysis framework spanning the multiscale nature of the VTB is presented herein. This hierarchical analysis framework employs the following micromechanical methods: the 3D parametric high-fidelity generalized method of cells (HFGMC) as well as the 3D sublaminate model. At the nanoscale level, the 3D HFGMC method is applied to obtain the effective elastic properties of a representative unit cell (RUC) representing the mineral collagen fibrils composite. Next at the submicron scale level, the 3D sublaminate model is used to generate the effective elastic properties of a repeated stack of multilayered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron scale level, the 3D HFGMC method is used again on a RUC of the highly porous VTB microstructure. The VTB-RUC geometries are taken from microcomputed tomography scans of VTB samples harvested from different vertebrae of human cadavers [Formula: see text]. The predicted anisotropic overall elastic properties for native VTBs are, then, examined as a function of age and sex. The predicted results of the VTBs longitudinal Young's modulus are compared to reported values found in the literature. The proposed 3D nested modeling analysis framework provides a good agreement with reported values of Young's modulus of single trabeculae as well as for VTB-RUC in the literature.

Identification of couple-stress moduli of vertebral trabecular bone based on the 3D internal architectures.

The purpose of this paper is to develop a homogeneous, orthotropic couple-stress continuum model as a substitute of the 3D periodic heterogeneous cellular solid model of vertebral trabecular bone. Vertebral trabecular bone is modeled as a porous material with an idealized periodic structure made of 3D open cubic cells, which is effectively orthotropic. The chosen architecture is based on studies of samples taken from the central part of vertebral bodies. The effective properties are obtained based on the response of the representative volume element under prescribed boundary conditions. Mixed boundary conditions comprising both traction and displacement boundary conditions are applied on the structure boundaries. In this contribution, the effective mechanical constants of the effective couple-stress continuum are deduced by an equivalent strain energy method. The characteristic lengths for bending and torsion are identified from the resulting homogenized orthotropic moduli. We conduct this study computationally using a finite element approach. Vertebral trabecular bone is modeled either as a cellular solid or as a two-phase material consisting of bone tissue (stiff phase) forming a trabecular network, and a surrounding soft tissue referring to the bone marrow present in the pores. Both the bone tissue forming the network and the pores are assumed to be homogeneous linear elastic, and isotropic media. The scale effects on the predicted couple stress moduli of these networks are investigated by varying the size of the bone specimens over which the boundary conditions are applied. The analysis using mixed boundary conditions gives results that are independent of unit cell size when computing the first couple stress tensor, while it is dependent on the cell size as to the second couple stress tensor moduli. This study provides overall guidance on how the size of the trabecular specimen influence couple stresses elastic moduli of cellular materials, with focus on bones. The developed approach is quite general and applicable to any heterogeneous cellular and composite materials.