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.
Highlights
Collagen arrangement can be described by the quarter stagger-overlap configuration proposed by Hodge and Petruska[11], that leads to a pattern of gap and overlap regions in the longitudinal direction of the fibril
Atomic Force Microscope imaging[16] showed that, in the longitudinal direction of the fibril, the apatite minerals replicate the periodicity of the collagen matrix
We determined the diffusion coefficient of water assuming a concentration gradient parallel to the three axes, i.e. L, W, T, of a global coordinate system (CST) fixed to the main axes of the trabecula, compliance with the system of reference used in the previous computational study[28]
Summary
Collagen arrangement can be described by the quarter stagger-overlap configuration proposed by Hodge and Petruska[11], that leads to a pattern of gap and overlap regions in the longitudinal direction of the fibril. We represent four unit cells of bone nanostructure in order to highlight the spatial arrangement of the mineral embedded in the collagen fibrils. Each unit cell is composed by three apatite platelets disposed in a staggered configuration along the longitudinal axis. The present model considers a staggered arrangement including overlapping of the apatite crystals in the longitudinal direction, while in the thickness and width direction parallel layers are assumed, in agreement with the studies of Hodge and Petruska[11] and Vercher-Martinez et al.[23]. We analyse free bone water at the collagen-apatite level of porosity (about 10 nm)[26] that contributes to important processes in mineralization, bone growth and healing through the transmission of remodelling signals[3] or plays a structuring role by orienting apatite crystals[27]
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