The Role Played by the Extra-Fibrillar Volume in the Structural and Mechanical Properties of Bones

<br/>Due to their complex network of distinct physical structures at different length scales, bones are responsible for body support, structure, motion, and several other functions for many different life forms. At the nanoscale scale, bones can be characterized as a fiber composite, i.e., a bundle of mineralized collagen fibrils surrounded by a matrix of water and calcium minerals. Different fractions of these constituents lead to different bone mechanical properties, making each bone unique, thus patient-specific.<br/>It is well established in the literature that a higher concentration of mineral content leads to superior mechanical properties, i.e., stiffer bones. Moreover, most of the mineral content in bones, about 80%, is found in the matrix surrounding the fibrils, also labeled the extra-fibrillar volume (EFV). However, the literature presents models that include minerals in the intra-fibrillar volume (IFV) only, models that resemble mineralized collagen fibrils.<br/>In this study, we investigate the structural and mechanical properties of all-atom bone molecular models constituted of type-I collagen, hydroxyapatite, and water through molecular dynamics (MD) simulations. Our models resemble fibers in bones, they encompass an EFV, explore different degrees of mineralization, and consider mineral content in both the EFV and the IFV, consistent with experimental observations presented in the literature. An analysis of the radial distribution function reveals that the local tetrahedral order of water is lost in similar ways in the EFV and IFV regions for all mineralized models, as calcium and phosphate ions are strongly coordinated with water molecules. By performing MD simulations using LAMMPS, we subject our models to uniaxial tensile loads and analyze their mechanical response. An analysis of the spatial stress distribution shows that the EFV plays a crucial role in the mechanical response of bone fibers. Both mineral and water content concentrate higher stresses when located in the EFV. Our results also corroborate the well-established finding that high mineral content makes bone stiffer. Our study reveals the EFV, which has been only recently contemplated in all-atom models, as an essential region to be considered when studying the mechanical properties of bones at the nanoscale. The mechanical properties of bones at such small scales can directly affect the properties at higher length scales, making bone more or less prone to fracture. Further development and studies on such elaborate all-atom models can give us additional insight into deformation and failure processes in bone, leading to a better understanding of bone diseases like osteoporosis.