Homogenization of heterogeneous tissue scaffold: A comparison of mechanics, asymptotic homogenization, and finite element approach

Actual prediction of the effective mechanical properties of tissue scaffolds is very important for tissue engineering applications. Currently common homogenization methods are based on three available approaches: standard mechanics modeling, homogenization theory, and finite element methods. Each of these methods has advantages and limitations. This paper presents comparisons and applications of these approaches for the prediction of the effective properties of a tissue scaffold. Derivations and formulations of mechanics, homogenization, and finite element approach as they relate to tissue engineering are described. The process for the development of a computational algorithm, finite element implementation, and numerical solution for calculating the effective mechanical properties of porous tissue scaffolds are also given. A comparison of the results based upon these different approaches is presented. Parametric analyses using the homogenization approach to study the effects of different scaffold materials and pore shapes on the properties of the scaffold are conducted, and the results of the analyses are also presented.