Multiscale Simulation and Validation of the Elastic Microstructure of Vertebral Bodies

骨质疏松性骨质流失及其相关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。本文将考虑一种多网格复合有限元方法来求解三维海绵体微观结构的Lame-Navier弹性方程，其中几何细节通过特殊的形状函数纳入有限元离散化。因此，避免了复杂且耗时的三维段边界的显式二维网格划分和段域内部的三维网格生成。模拟将通过泡沫铝、牛和人类小梁骨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，并可能导致更早、更准确地发现需要适当治疗骨质疏松性骨质流失的患者。

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.