A Stochastic Structural Finite Element Model for Trabecular Bone and other Structural Foams

Abstract

Background: Although trabecular bone is a highly porous heterogeneous composite, most studies use homogenized continuum finite element (FE) approaches to model trabecular bone. Such models neglect the porous nature of the tissue. When microstructural models are desired, the use of continuum elements may require costly CT/MRI imaging and detailed meshing. The purpose of this study is to demonstrate an approach that simulates trabecular bone with less dependency on medical images while capturing the effect of porosity. Methods: A stochastic structural FE model was created representing the trabecular micro-architecture as beam elements. Beam orientation, length and connectivity were stochastically determined by random placement of nodes and meshing the resulting Voronoi diagram. Boundary conditions were applied on the structure to attain normalized axial and shear strain. Also, apparent mechanical properties, apparent densities and anisotropy ratios were calculated from the model output. Results: The number of generated seeds within the model and cross sectional area of the random beams were observed as parameters that affect model outcome. The apparent mechanical properties and apparent densities were found to be sensitive to number of beams; beams mean length and beams cross sectional area. Clinical Relevance: The proposed finite element technique provides a stochastically accurate structural representation of trabecular tissue and its reaction to applied loads. It incorporates several advantages of high fidelity methods but at lower cost and requiring only clinical imaging. Therefore, this approach may be useful for patient specific musculo-skeletal biomechanical modeling.