弹性模量与表观密度的分段函数关系用于股骨近端的结构模拟

目前，在用功能适应性理论与有限元相结合，进行计算机数值模拟骨再造时，大多数研究者对于不同的表观密度，都是将表观密度和弹性模量的关系取为一种形式。由于松质骨的各向异性，其结构形式的多样性、复杂性，认为用一个统一的模型来描述其结构性能存在一定的问题。本研究基于松质骨胞元模型理论，提出与实际更加接近的松质骨弹性模量与表观密度的分段函数关系，使得弹性模量与表观密度关系的确立有一定的理论基础。利用Mullender等提出的骨自我组织控制过程微分方程来控制骨再造过程，与有限元相结合，将这种松质骨的弹性模量与表观密度的分段函数关系应用到股骨近端结构的模拟预测中，不但能根据模拟得到的内部密度分布给出其内部结构的具体胞元结构形式，而且可以大大提高迭代的收敛速度，因此是一项具有一定的理论意义和实际应用价值的工作。

APPLICATION OF SUBSECTIONAL RELATIONSHIP BETWEEN ELASTIC MODULUS AND APPARENT DENSITY IN THE STRUCTURAL SIMULATION OF PROXIMAL FEMUR

Nowadays most authors take the relationship between elastic modulus and apparent density as the only form for different apparent densities when they simulate bone remodeling numerically by combining bone functional adaptation with FEM. We believe it problematic to describe the structure of trabecular bone using such an uniform model because of its diversity and complexity. Based on the theory of microstructures in cancellous bone, a subsectional relationship between elastic modulus and apparent density which may be closer to reality is put forward, to serve as a theoretical basis for the establishment of the relationship between elastic modulus and apparent density. The self organizational control process put forward by Mullender et al. (1994) was used to control the remodeling process to integrate with FEM and the subsectional relationship between elastic modulus and apparent density applied to the structural simulation of proximal femur. Not only the inner micromechanical structures were acquired according to the internal density distribution simulated, but the converge speed of iteration was greatly increased. It is a job with certain theoretical significance and practical value.