Hole in One: an element reduction approach to modeling bone porosity in finite element analysis

Finite element analysis has been an increasingly widely applied biomechanical modeling method in many different science and engineering fields over the last decade. In the biological sciences, there are many examples of FEA in areas such as paleontology and functional morphology. Despite this common use, the modeling of trabecular bone remains a key issue because their highly complex and porous geometries are difficult to replicate in the solid mesh format required for many simulations. A common practice is to assign uniform model material properties to whole or portions of models that represent trabecular bone. In this study we aimed to demonstrate that a physical, element reduction approach constitutes a valid protocol for addressing this problem in addition to the wholesale mathematical approach. We tested a customized script for element reduction modeling on five exemplar trabecular geometry models of carnivoran temporomandibular joints, and compared stress and strain energy results of both physical and mathematical trabecular modeling to models incorporating actual trabecular geometry. Simulation results indicate that that the physical, element reduction approach generally outperformed the mathematical approach: physical changes in the internal structure of experimental cylindrical models had a major influence on the recorded stress values throughout the model, and more closely approximates values obtained in models containing actual trabecular geometry than solid models with modified trabecular material properties. In models with both physical and mathematical adjustments for bone porosity, the physical changes exhibit more weight than material properties changes in approximating values of control models. Therefore, we conclude that maintaining or mimicking the internal porosity of a trabecular structure is a more effective method of approximating trabecular bone behavior in finite element models than modifying material properties.