Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies

• Applicant: Professor Dr. Martin Rumpf
• Subject Area: Mathematics
• Term: from 2005 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5446327

Osteoporotic bone loss and the associated occurrence of fragility fractures is one of the most serious future burdens of our aging society. We will develop the mathematical and algorithmic tools for a reliable simulation of the elastic properties of vertebral bodies and validate the results with experiments. A multigrid composite finite element approach will be considered for the Lame-Navier equations of elasticity on the micro structure of the spongiosa in 3D, where geometric details are incorporated in a finite element discretization via special shape functions. Hence, the complicated and time-consuming explicit 2D meshing of 3D segment boundaries and a 3D grid generation for the interior of the segment domains is avoided. The simulations will be validated with experiments for aluminum foams, bovine and human trabecular bone specimens, and complete human vertebral bodies.This approach will lead to an improvement in the ability to predict the future risk of fractures and may lead to earlier and more accurate detection of patients that require adequate treatment for osteoporotic bone loss.

• DFG Programme: Research Grants
• International Connection: Switzerland
• Participating Person: Professor Dr. Stefan Sauter