Hierarchical 3D models of the mineralized collagen fibrils

Bone tissue is characterized by a remarkable hierarchical structure, from nano – to macro – scale. The structural organization of bone is based on the nanoscale building block, i.e. the mineralized collagen fibril, mainly composed of type I collagen, apatite minerals and water. The properties at the nanoscale define the behaviour of the macroscale. Several experimental techniques have been used to assess the arrangement of bone components at the nanoscale, but information is still elusive due to resolution limits. Computational modelling can be used as a complementary method to model and quantify the main nanoscale mechanisms that influence the properties of bone tissue. This Thesis aims to provide further insights into the nanostructure of human bone tissue. An initial 3D model of a unit cell of the mineralized collagen fibril is developed based on the 2D models available in Literature. Subsequently, a system of equations is implemented to describe the diffusion phenomenon at the collagen-apatite level of porosity. Monte Carlo method is used to consider the majority of the unit cell geometric characteristics and possible flow paths in the three main directions of a coordinate system aligned with the axes of a single trabecula. The outcomes allow to assess the orientation of the apatite platelets and to provide information concerning structural factors that mainly influence water diffusion within the mineralized collagen fibril. A further step of this Thesis concerns the development of a 3D geometric model of the entire mineralized collagen fibril. The study aims to analyse the effects of the mineral volume fraction on the organization of the nanostructure by means of the continuum percolation theory. The latter is a pillar of statistical physics that studies the connectivity in a system. It is the first attempt to determine whether the mineralized collagen fibril may develop an extended network of connected apatite minerals. The methodology of the continuum percolation is adapted to the geometry of the mineralized collagen fibril and the Monte Carlo method is implemented for ten different mineral volume fractions. The outcomes provide evidence that for hypermineralized conditions, the number of extended network of minerals increases. Therefore, an abnormal mineral arrangement at the nanostructure may contribute to the critical behaviour of the tissue. The outcomes of the presented research related to the apatite arrangement at bone nanoscale may facilitate the design and optimization of bio-scaffolds for tissue engineering. In-depth knowledge of bone nanostructure is essential to enhance the longevity of bio-scaffolds and to decrease the risk of failure.