Modeling Osteoporotic Spongy Bone Using Cellular Structures

The mechanical properties of spongy bone are a function of the tissue's microstructure including the strength and microarchitecture of the trabeculae. The thickness and number of trabeculae (morphological data) are the most important parameters that can indicate the porosity of tissue. Osteoporosis is known as a decrease in the thickness or loss of trabeculae that causes a reduction in the density and strength of bone. This research aims to model osteoporosis using cellular (lattice) structures and also presents mechanical relationships to predict tissue behavior during osteoporosis using morphological data for spongy tissue. Experimental trendlines (Young's modulus and relative density) are developed and equivalent lattice structures for osteoporotic spongy bone are presented using eight different types of unit cells such as cubic, hexagonal, tesseract, diamond, BCC, truncated cube, octahedral, and rhombic dodecahedron. Also, structural damage modes including trabeculae thinning, trabeculae elimination, and hybrid mode are implemented for determining the optimum geometrical characteristics of lattice structures for modeling osteoporosis. Comparison between normalized elastic moduli for unit cell structures indicates that the diamond unit cell exhibits less than 5% difference with experimental values. Also, for a reduction of relative density from 0.3 to 0.1 as a result of the hybrid damage mode, the normalized elastic moduli of the diamond numerical model and experimental result were reduced by about 0.013 and 0.0186, respectively. Finally, results show that among all the unit cell types, the diamond unit cell when used alongside the hybrid damage mode can predict the osteoporosis behavior of bone with the best accuracy.