Finite element analysis of idealised unit cell cancellous structure based on morphological indices of cancellous bone

Abstract

Human bones can be categorised into one of two types—the compact cortical and the porous cancellous. Whilst the cortical is a solid structure macroscopically, the structure of cancellous bone is highly complex with plate-like and strut-like structures of various sizes and shapes depending on the anatomical site. Reconstructing the actual structure of cancellous bone for defect filling is highly unfeasible. However, the complex structure can be simplified into an idealised structure with similar properties. In this study, two idealised architectures were developed based on morphological indices of cancellous bone: the tetrakaidecahedral and the prismatic. The two architectures were further subdivided into two types of microstructure, the first consists of struts only and the second consists of a combination of plates and struts. The microstructures were transformed into finite element models and displacement boundary condition was applied to all four idealised cancellous models with periodic boundary conditions. Eight unit cells extracted from the actual cancellous bone obtained from micro-computed tomography were also analysed with the same boundary conditions. Young’s modulus values were calculated and comparison was made between the idealised and real cancellous structures. Results showed that all models with a combination of plates and struts have higher rigidity compared to the one with struts only. Values of Young’s modulus from eight unit cells of cancellous bone varied from 42 to 479 MPa with an average of 234 MPa. The prismatic architecture with plates and rods closely resemble the average stiffness of a unit cell of cancellous bone.