Multiscale modeling of elastic properties of trabecular bone

We model trabecular bone as a composite material with hierarchical structure. At a nanostructural level, bone is composed of collagen molecules containing water and non-collagenous proteins in their gaps reinforced with hydroxyapatite nanocrystals. At a sub-microstructural level (few microns), the mineralized collagen fibrils are embedded in an extrafibrillar hydroxyapatite matrix to form a single lamella, which also contains lacunar cavities. At a microstructural level (hundreds of microns), several lamellae are randomly orientated in different orientations to form trabecular pockets forming a single trabecula. At a mesostructural level (several millimeters), the trabecular bone is represented by a porous random network of trabeculae. In this paper we predict analytically the effective elastic constants of trabecular bone by modeling its elastic response at these different scales, spanning from the nanostructural to mesostructural levels, using micromechanics methods and composite materials laminate theories. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The predictions are in good agreement with the experimental data reported in literature.