Percolation networks inside 3D model of the mineralized collagen fibril

Bone is a hierarchical biological material, characterized at the nanoscale by a recurring structure mainly composed of apatite mineral and collagen, i.e. the mineralized collagen fibril (MCF). Although the architecture of the MCF was extensively investigated by experimental and computational studies, it still represents a topic of debate. In this work, we developed a 3D continuum model of the mineral phase in the framework of percolation theory, that describes the transition from isolated to spanning cluster of connected platelets. Using Monte Carlo technique, we computed overall 120 × 10⁶ iterations and investigated the formation of spanning networks of apatite minerals. We computed the percolation probability for different mineral volume fractions characteristic of human bone tissue. The findings highlight that the percolation threshold occurs at lower volume fractions for spanning clusters in the width direction with respect to the critical mineral volume fractions that characterize the percolation transition in the thickness and length directions. The formation of spanning clusters of minerals represents a condition of instability for the MCF, as it could be the onset of a high susceptibility to fracture. The 3D computational model developed in this study provides new, complementary insights to the experimental investigations concerning human MCF.