Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies

骨质疏松性骨丢失和相关的脆性骨折的发生是我们老龄化社会最严重的未来负担之一。我们将开发数学和算法工具，用于可靠地模拟椎体的弹性特性，并通过实验验证结果。一个多重网格复合有限元方法将被考虑为三维的海绵体的微观结构上的Lame-Navier方程的弹性，几何细节被纳入通过specialshape函数的有限元离散。因此，避免了复杂且耗时的3D段边界的显式2D网格化和段域内部的3D网格生成。该模拟将通过泡沫铝、牛和人类松质骨标本以及完整的人类椎体的实验进行验证。这种方法将提高预测未来骨质疏松风险的能力，并可能导致更早和更准确地检测需要适当治疗骨质疏松性骨丢失的患者。

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.