A Comparison of Hexahedral and Tetrahedral Finite Elements for Biphasic Analysis of Cartilage Micromechanics

Articular cartilage is a hydrated composite structure comprised of collagen type II extracellular matrix (ECM), collagen type VI pericellular matrix (PCM), and chondrocytes, each with low hydraulic permeability resulting in long viscoelastic stress relaxation times. Therefore, when subjected to fast loading, cartilage behaves as a nearly incompressible material [1]. When finite element analysis (FEA) is employed to solve mechanical problems involving nearly incompressible materials, a hexahedral finite element mesh is desirable [2]. Unfortunately, hexahedral mesh generation is difficult for complex geometries and often requires painstaking user-assisted construction which is often not feasible. Realistic chondron shapes and distributions within cartilage exhibit this complexity [3]. In these scenarios, a tetrahedral finite element discretization may need to be employed (Figure 1).