U. Wolfram, L. O. Schwen, U. Simon, M. Rumpf, and H.-J. Wilke.
Statistical osteoporosis models using composite finite elements: A
Journal of Biomechanics, 42(13):2205-2209, September 2009.
[ bib | DOI | .pdf 1 ]
Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, numerous researchers employ micro finite element models. To avoid disadvantages in setting up classical finite element models, composite finite elements can be used. The aim of the study is to test the potential of composite finite elements. Furthermore, we are interested in whether changing trabecular diameters or losing trabeculae reduces macroscopic stiffness more. For that, a parameter study on numerical lattice samples with statistically simulated, simplified osteoporosis is performed. These samples are subjected to compression and shear loading. Results show that the worst drop of compressive stiffness is reached for transverse isotropic structures under 32% isotropic trabecular degradation (89.7% loss of the initial stiffness). Whereas the worst drop in shear stiffness is found for slightly transverse isotropic structure subjected to isotropic trabecular degradation of 32% (67.6% of the initial stiffness). The study indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. The results further demonstrate that composite finite elements are an efficient simulation tool for micro-structured samples.