Multiscale approach incorporating tropocollagen scale to assess the effect of molecular age-related modifications on elastic constants of cortical bone based on finite element and homogenization methods.

With osteoporosis and aging, structural changes occur at all hierarchical levels of bone from the molecular scale to the whole tissue, which requires multiscale modeling to analyze the effect of these modifications on the mechanical behavior of bone and its remodeling process. In this paper, a novel hybrid multiscale model for cortical bone incorporating the tropocollagen molecule based on the combination of finite element method and different homogenization techniques was developed. The objective was to investigate the influence of age-related structural alterations that occur at the molecular level, namely the decrease in both molecular diameter (due to the loss of hydration) and number of hydrogen bonds, on mechanical properties of the bone tissue. The proposed multiscale hierarchical approach is divided in two phases: (i) in Step 0, a realistic 3D finite element model for tropocollagen was used to estimate the effective elastic properties at the molecular scale as a function of the collagen molecule's degree of hydration (represented by its external diameter) and the number of its intramolecular hydrogen bonds, and (ii) in Steps 1-10, the effective elastic constants at the higher scales from mineralized fibril to continuum cortical bone tissue were predicted analytically using homogenization equations. The results obtained in healthy mature cortical bone at different scales are in good agreement with the experimental data and multiscale models reported in the literature. Moreover, our model made it possible to visualize the influence of the two parameters (molecular diameter and number of hydrogen bonds) that represent the main age-related alterations at the molecular scale on the mechanical properties of cortical bone, at its different hierarchical levels. Keywords: Bone aging, multiscale model, tropocollagen, cortical bone, finite element modeling, homogenization method.

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