Adapting Metamaterial Structures for a New Generation of Bone Substitute Scaffolds with the Desired Stiffness and Permeability: A Finite Element Analysis

This study investigated the design of bone replacement scaffolds using metamaterial structures with finite element analysis. On this basis, four scaffolds with metamaterial architecture, namely Chiral, Chiral-Truss, Re-entrant, and QSH, each with five different porosities of 70, 75, 80, 85, and 90%, were designed, and a total of 20 models were obtained. Given that the mechanical characteristics, especially the stiffness of a scaffold for bone, play an essential role in its success, the elastic modulus of the models was investigated in this study. The effective elastic modulus and Poisson's ratio were calculated using the finite elements method. The scaffold material was selected as titanium alloy, and the models showed an effective elastic modulus between 1 and 15 GPa. Another aspect of a scaffold design is its permeability and fluid flow modality. The permeability of the designed scaffolds was calculated by performing a CFD analysis using Darcy's law. The computed permeability was in 1.3-25x10-9m2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.3-25{\times 10}<^>{-9}{m}<^>{2}$$\end{document} intervals. Moreover, the average fluid flow-induced wall shear stress in the scaffolds was determined, and the results showed that its magnitude depended on the scaffold architecture and porosity. The elastic modulus results indicated the success of the models in satisfying the human bone stiffness requirements. Also, the permeability results of the models were consistent with those reported for human trabecular bone. This study investigated a scaffold design using the metamaterial features comprehensively from both stiffness and fluid flow modality aspects at the same time. The outcomes of this study shed light on the design and development of new scaffolds with metamaterial properties.