3D tortuosity and diffusion characterization in the human mineralized collagen fibril using a random walk model

Bone tissue is mainly composed at the nanoscale of apatite minerals, collagen molecules and water that form the mineralized collagen fibril (MCF). In this work, we developed a 3D random walk model to investigate the influence of bone nanostructure on water diffusion. We computed 1000 random walk trajectories of water molecules within the MCF geometric model. An important parameter to analyse transport behaviour in porous media is tortuosity, computed as the ratio between the effective path length and the straight-line distance between initial and final points. The diffusion coefficient is determined from the linear fit of the mean squared displacement of water molecules as a function of time. To achieve more insight into the diffusion phenomenon within MCF, we estimated the tortuosity and diffusivity at different quotes in the longitudinal direction of the model. Tortuosity is characterized by increasing values in the longitudinal direction. As expected, the diffusion coefficient decreases as tortuosity increases. Diffusivity outcomes confirm the findings achieved by experimental investigations. The computational model provides insights into the relation between the MCF structure and mass transport behaviour that may contribute to the improvement of bone-mimicking scaffolds.