A multiscale finite element investigation on the role of intra- and extra-fibrillar mineralisation on the elastic properties of bone tissue

Abstract

Lamellar bone is one of the fundamental structural units of bone tissue and it consists of mineralised collagen fibrils (MCFs) embedded within an extra-fibrillar matrix comprised of hydroxyapatite minerals distributed throughout a matrix of non-collagenous proteins (NCPs). While both intra- and extra-fibrillar phases provide a critical contribution to tissue-level behaviour, the mechanical implications of their structural arrangement, and in particular the relative distribution of HA minerals between both phases, remains poorly understood. This study presents a multiscale finite element framework to investigate the role of intra- and extra-fibrillar mineralisation on the elastic properties of bone tissue by considering two levels of structural hierarchy. At the nanoscale, representative volume elements (RVEs) of both MCFs and the extra-fibrillar matrix were developed, and a homogenisation strategy was used to determine the effective elastic properties of each phase. At the sub-micron level, an RVE of lamellar bone that accounted for newly reported patterns of mineral platelets encircling collagen fibrils was used to predict the effective response of lamellar bone tissue, with material properties established from the previous length scale. The results demonstrated that the overall mineral content in the tissue is the biggest contributor to the effective elastic properties of lamellar bone. While this is perhaps unsurprising, importantly, it was demonstrated that the extra-fibrillar matrix (and mineral therein) is the phase that makes the primary contribution to the elastic response of the tissue. The two main reasons that the extra-fibrillar matrix dominated the load-bearing response are (i) the greater proportion of mineral content compared to the intra-fibrillar regions and (ii) the highly ordered arrangement of mineral platelets that are aligned to the longitudinal axis of MCFs. Both of these features resulted in extra-fibrillar mineral strain ratios that were consistently higher than intra-fibrillar mineral strain ratios under axial loading. As a result, the predicted elastic properties of MCFs were much lower than the extra-fibrillar matrix, indicating that intra-fibrillar mineralisation only provided a modest contribution to the stiffness of bone tissue. Collectively, the predicted results of the multiscale approach compared well to the range properties measured through various experimental testing methods, highlighting its potential to provide further insight into the role of sub-tissue features of tissue biomechanics.

Keywords: Bone sub-microstructure; Extra-fibrillar matrix; Finite element homogenisation; Lamellar bone; Mineralised collagen fibrils.