3D diffusion model within the collagen apatite porosity: an insight to the nanostructure of human trabecular bone

Bone tissue at nanoscale is a composite mainly made of apatite crystals, collagen molecules and water. This work is aimed to study the diffusion within bone nanostructure through Monte-Carlo simulations. To this purpose, an idealized geometric model of the apatite-collagen structure was developed. Gaussian probability distribution functions were employed to design the orientation of the apatite crystals with respect to the axes (length L, width W and thickness T) of a plate-like trabecula. We performed numerical simulations considering the influence of the mineral arrangement on the effective diffusion coefficient of water. To represent the hindrance of the impermeable apatite crystals on the water diffusion process, the effective diffusion coefficient was scaled with the tortuosity, the constrictivity and the porosity factors of the structure. The diffusion phenomenon was investigated in the three main directions of the single trabecula and the introduction of apatite preferential orientation allowed the creation of an anisotropic medium. Thus, different diffusivities values were observed along the axes of the single trabecula. We found good agreement with previous experimental results computed by means of a genetic algorithm.