Anisotropic Permeability of Trabecular Bone and its Relationship to Fabric and Architecture: A Computational Study.

Trabecular bone is a porous, mineralized tissue found in vertebral bodies, the metaphyses and epiphyses of long bones, and in the irregular and flat shaped bones. The pore space is filled with bone marrow, a highly cellular fluid. Together, the bone and marrow behave as a poroelastic solid. In poroelasticity theory, the permeability is the primary material property that governs the momentum transfer between the solid and fluid constituents. In the linearized theory, the permeability of a material depends on the shape and connectivity of the pores. Developing a model of the relationship between trabecular microarchitecture and permeability could lead to improved simulations of trabecular bone mechanical response, which can be used to investigate bone adaptation, mechanobiological signaling, and progression of diseases such as osteoporosis. This study used finite element models of the trabecular pore space to calculate the complete anisotropic permeability tensor of 12 human and 18 porcine femoral trabecular bone samples. The sensitivity of the simulations to model assumptions and post-processing was analyzed to improve confidence in the result. The orthotropic permeability tensor depended on the fabric tensor, trabecular spacing, and structure model index through a power law relationship. Porosity and fabric alone also provided a reasonable prediction, which may be useful in cases where the image resolution is insufficient to obtain detailed measures of architecture.

Mechanical stimulation of bone marrow in situ induces bone formation in trabecular explants.

Low magnitude high frequency (LMHF) loading has been shown to have an anabolic effect on trabecular bone in vivo. However, the precise mechanical signal imposed on the bone marrow cells by LMHF loading, which induces a cellular response, remains unclear. This study investigates the influence of LMHF loading, applied using a custom designed bioreactor, on bone adaptation in an explanted trabecular bone model, which isolated the bone and marrow. Bone adaptation was investigated by performing micro CT scans pre and post experimental LMHF loading, using image registration techniques. Computational fluids dynamic models were generated using the pre-experiment scans to characterise the mechanical stimuli imposed by the loading regime prior to adaptation. Results here demonstrate a significant increase in bone formation in the LMHF loaded group compared to static controls and media flow groups. The calculated shear stress in the marrow was between 0.575 and 0.7 Pa, which is within the range of stimuli known to induce osteogenesis by bone marrow mesenchymal stem cells in vitro. Interestingly, a correlation was found between the bone formation balance (bone formation/resorption), trabecular number, trabecular spacing, mineral resorption rate, bone resorption rate and mean shear stresses. The results of this study suggest that the magnitude of the shear stresses generated due to LMHF loading in the explanted bone cores has a contributory role in the formation of trabecular bone and improvement in bone architecture parameters.