Mathematical Quantification of the Impact of Microstructure on the Various Effective Properties of Bones

Abstract

Abstract The goal of this paper is to quantify the influence of microstructure on effective properties of cancellous bones by the fabric tensor, a tool well developed in the biomedical community and by the integral representation formula (IRF), which is well studied in the mathematical materials science community. The focus is on permeability tensor and the tortuosity tensor. The implications of IRF on the viscodynamic properties of the poroelastic composites is discussed from an analytical point of view. Numerical calculations of the fabric tensors and the static permeability tensors of three cancellous bone samples are also presented. Future direction for combining the advantages of both approaches is also discussed in this paper.