Effects of architecture, density and connectivity on the properties of trabecular bone: a two-dimensional, Voronoi cell based model study

Abstract

Trabecular bone, rather than being considered as a homogeneous material, must be analysed as a structure of interconnected beam and plate-like elements. The arrangement and morphology of these elements depend on the specific tissue studied as well as on the physiology of the individual. It is therefore impossible to define the mechanical properties trabecular bone in general. To estimate the properties of an individual structure, flexible numerical models must be developed, which allow the calculation of elastic constants and resistance of tissue previously characterised by non-destructive observation. Voxel-based modelling of structures observed by X-ray microtomography is computation intensive. Here, synthetic 2D-microstructures are analysed, constructed as a collection of Voronoi-cells obtained from the observation of plane sections of cancellous bone. The effect of architecture (vertebra and femur), bone density and loss of trabecular connectivity was researched. The study confirms findings of earlier experimental and numerical studies relating to the effect of these parameters; the technique is efficient in terms of experimental effort and numerical analysis. Consequently, the use of synthetic microstructures based on a Voronoi-cell approximation of the real bone architecture may be a promising approach for the prediction of the mechanical properties of trabecular bone.

The effect of bone marrow on the mechanical behavior of porcine trabecular bone

“…This suggests that the samples without bone marrow have a higher stiffness and, as the interstitial flow through the trabecular structure is less viscous, it can more readily flow out through the structure without causing damage. Therefore, during the deformation, the compression of the bone marrow in the vertical direction would cause the (incompressible, more viscous, non-Newtonian) fluid to bulge in the horizontal direction, therefore bending the trabecula and reducing the apparent strength (Ruiz et al 2011). This does not happen in the samples without the bone marrow, where the (less viscous) saline solution does not pose an immediate additional lateral stress on the trabeculae.…”

“…This most likely would result in higher hydrostatic pressure inside the structure and lower values of the measured mechanical properties. Moreover, the intertrabecular regions are not always connected, and so removing the bone marrow would promote hinging and bending of the trabecula (Ruiz et al 2011). When the marrow is inside the pores of the trabecular structure, the limited flow causes the internal pressure to rise, resulting in higher localized stress and a premature failure of the trabeculae.…”

Comportamiento biomecánico de tejido óseo en fijaciones de columna

“…The configuration of the trabeculae changes in each type of bone and within the same bone [20][21][22] . It is suggested that the modulus of elasticity (E) of the vertebral tissue is approximately 1 GPa, the great dispersion of values in this tissue is influenced not only by the stiffness of the trabecula but also by its orientation or disposition [23][24][25] . Banse et al 26 limited the yield stress range between 0.6 and 6.17 MPa.…”

A morphological, topological and mechanical investigation of gyroid, spinodoid and dual-lattice algorithms as structural models of trabecular bone

“…Recently, studies have included greater complexity when using computational approaches to generate biomimetic trabecular bone structures in an effect to better represent the morphological and topological features of the trabecular bone microarchitecture. Early work by Gibson and coworkers has used Voronoi tessellation in two- (Ruiz et al, 2011(Ruiz et al, , 2010Schaffner et al, 2000;Silva and Gibson, 1997) and three-dimensions (Chao et al, 2021;Kirby et al, 2020) to create irregular cellular solid representations for low-density trabecular bone (Makiyama et al, 2002;Vajjala et al, 2000).…”