Background: Although trabecular bone is 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 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 ratio’s were calculated from the model output.
Results: The number of generated nodes within the model and cross sectional area of the random beams were observed as parameters that affect model outcome. Trabecular bone apparent density was found highly correlated to beams cross sectional area rather than the generated number of nodes. Similarly, Young’s moduli and shear moduli were dependent on beams cross sectional area. For example, a (0.015 mm2) increase in beam cross section area can produce (175 MPa, 30 MPa and 0.55 g/cm3) increases in Young’s moduli, shear moduli and apparent density, respectively.
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, the approach may be useful for patient specific musculo-skeletal biomechanical models (e.g. osteoporosis, osteoarthritis, joint replacement and implants interface).
