Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies

骨质疏松性骨丢失和与之相关的脆性骨折的发生是我们老龄化社会未来最严重的负担之一。我们将开发数学和算法工具，以可靠地模拟椎体的弹性特性，并通过实验验证结果。采用多重网格组合有限元方法求解三维海绵微结构的Lame-Navier弹性方程，其中几何细节通过特殊的形函数结合到有限元离散中。因此，避免了复杂且耗时的3D分段边界的显式2D网格划分和分段区域内部的3D网格生成。这些模拟将通过对泡沫铝、牛和人的骨小梁标本以及完整的人类椎体的实验来验证。这种方法将提高预测未来骨折风险的能力，并可能导致对需要适当治疗的骨质疏松性骨丢失的患者进行更早和更准确的检测。

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.