Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies

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