Multiscale modeling of human bone

Abstract

A multiscale modeling technique was developed to predict mechanical properties of human bone, which utilizes the hierarchies of human bone in different length scales from nanoscale to macroscale. Bone has a unique structure displaying high stiffness with minimal weight. This is achieved through a hierarchy of complex geometries composed of three major materials: hydroxyapatite, collagen and water. The identifiable hierarchical structures of bone are hydroxyapatite, tropocollagen, fibril, fiber, lamellar layer, trabecular bone, cancellous bone and cortical bone. A helical spring model was used to represent the stiffness of collagen. A unit cell-based micromechanics model computed both the normal and shear stiffness of fibrils, fibers, and lamellar layers. A laminated composite model was applied to cortical and trabecular bone, while a simplified finite element model for the tetrakaidecahedral shape was used to evaluate cancellous bone. Modeling bone from nanoscale components to macroscale structures allows the influence of each structure to be assessed. It was found that the distribution of hydroxyapatite within the tropocollagen matrix at the fibril level influences the macroscale properties significantly. Additionally, the multiscale analysis model can vary any parameter of any hierarchical level to determine its effect on the bone property. With so little known about the detailed structure of nanoscale and microscale bone, a model encompassing the complete hierarchy of bone can be used to help validate assumptions or hypotheses about those structures.