A 3D Model of the Effect of Tortuosity and Constrictivity on the Diffusion in Mineralized Collagen Fibril

Abstract

Bone tissue is a hierarchically structured material composed at the nanoscale by an organic matrix of collagen type I, apatite mineral and water. We considered an idealized 3D geometrical model of the mineralized collagen fibril in order to analyze the influence of structural factors, i.e. tortuosity, constrictivity, on the water effective diffusivity. The average values of the factors investigated in the diffusivity are computed on 5000 iterations by means of the Montecarlo method. The input parameters of the numerical model are the geometrical dimensions of the apatite mineral, collagen fibrils and their spatial orientation obtained with random extractions from Gaussian probability distribution functions. We analyzed the diffusion phenomenon for concentration gradients parallel to three orthogonal directions (Length, Width and Thickness) and for different scenarios, namely low, intermediate and high apatite volume fraction. For each degree of volume fraction, in the thickness direction, the tortuosity assumes greater values, up to two orders of magnitude, in comparison with the tortuous factors computed in the other directions, highlighting the anisotropy of the nanostructure. Furthermore, it was found that the tortuosity is the dominant parameter which control the effective transport properties within the mineralized collagen fibrils.