Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies
Final Report Abstract
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 and the impact on the macroscopic mechanical properties has been investigated. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, a Composite Finite Element (CFE) approach was applied. Also for scalar and vector-valued elliptic boundary value problems with discontinuous coef?cients across geometrically complicated interfaces, a CFE approach was developed. Composite basis functions were constructed, mimicing the expected jump condition for the solution at the interface in an approximate sense. The construction is based on a suitable local interpolation on the space of admissible functions. As applications, specimens of aluminium foam matrix ?lled with polymer and linear elasticity of microstructured materials, in particular specimens of trabecular bone, were investigated. Furthermore, in a parameter study on numerical lattice samples with statistically simulated degradation, the mechanical impact of simpli?ed osteoporosis models was evaluated. This study e.g. indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. Finally, a numerical homogenization approach was developed for real material specimens which are not strictly periodic but are considered as statistical prototypes. Thereby, effective macroscopic material properties can be computed. For larger samples of human, bovine, and porcine trabecular bone, the developed Finite Element tool box has been applied to analyze the macroscopic properties statistically.
Publications
- Finite element simulation of bone microstructures, Proceedings of the 14th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, University of Ulm, July 2007, pp. 52–66
Tobias Preusser, Martin Rumpf, and Lars Ole Schwen
- Determining effective elasticity parameters of microstructured materials, Proceedings of the 15th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, University of Ulm, July 2008, pp. 41–62
Lars Ole Schwen, Uwe Wolfram, Hans-Joachim Wilke, and Martin Rumpf
- Composite ?nite elements for 3D image based computing, Computing and Visualization in Science 12 (2009), no. 4, 171–188
Florian Liehr, Tobias Preusser, Martin Rumpf, Stefan Sauter, and Lars Ole Schwen
- Statistical osteoporosis models using composite ?nite elements: A parameter study, Journal of Biomechanics 42 (2009), no. 13, 2205–2209
Uwe Wolfram, Lars Ole Schwen, Ulrich Simon, Martin Rumpf, and Hans-Joachim Wilke
- Numerical homogenization of trabecular bone specimens using composite ?nite elements, 1st Conference on Multiphysics Simulation – Advanced Methods for Industrial Engineering, Fraunhofer, 2010
Martin Rumpf, Lars Ole Schwen, Hans-Joachim Wilke, and Uwe Wolfram
