椎体结构及其生长过程模拟  

SIMULATION ON THE STRUCTURE AND GROWTH OF VERTEBRA

作　　者：朱兴华[1] 宫赫[1] 朱东[2] 

机构地区：[1]吉林大学力学系,长春130025 [2]中国人民解放军208医院,长春130062

出　　处：《中国生物医学工程学报》2001年第4期310-316,304,共8页Chinese Journal of Biomedical Engineering

基　　金：国家自然科学基金资助项目 (3 9970 191);吉林省科技发展计划项目 (19980 5 5 4 0 1)

摘　　要：目前 ,关于骨自优化 ,或称自适应的定量描述 ,只有线性的骨再造速率方程 ,用它与有限元相结合去预测骨结构 ,仅限于在实测骨的外部几何形状基础上 ,预测其内部组织结构。至于骨的外部几何形状的模拟预测未见报道。本文的目的是利用骨自优化理论完成椎体的外部几何形状、内部组织结构及生长过程的模拟。采用了一种新的高阶非线性骨再造速率方程与有限元相结合 ,引入工程拓扑优化思想 ,从不确定的外形出发进行模拟 ;并且实测了人第三腰椎椎体冠状面的外部几何形状及内部组织结构。预测的结果在外部几何形状和内部组织结构上与实测相一致。外形上老年期比年轻期椎体具有更向内凹的腰鼓形 ,小梁骨主要沿主应力即垂直方向排列 ,只不过 ,老年期更疏松。是否可以说 ,采用这种自优化方程与有限元相结合 ,引入拓扑优化思想 ,不但能模拟预测骨的外部几何形状和内部组织结构 ,而且可以模拟其生长过程。尤其值得强调的是实现了外部几何形状的模拟 ,只有这样才能得以实现生长过程的模拟预测。At present there is only linear rate equation of bone remodeling to quantitatively describe bone′s self-optimization or self-adaptation. By combining it with FEM bone structure can be predicated. In literature several authors simulated internal bone architectures inside the real external shapes. But few results simulated on bone external shape have been reported. The aim of this paper was to simulate the external shape and internal structure of vertebra and its growth. A new high order nonlinear rate equation of bone remodeling combining with FEM was adopted in a uniform square plate, in which we imported topology optimization in engineering. We also measured the external shape and internal structure of the cross-section of the third lumber. The results simulated are consistent with practical measure in both external shape and internal structure. In old stage, its shape is more concave than that in young stage and its trabecular bone is disposed along the principal stresses, i.e, along vertical direction. The trabecular bone in old stage is merely much looser. Whether we can say it that by combining this self-optimizing equation with FEM, not only can we simulate and predict the external shape and internal structure of bone, but also simulate its growth with topology-optimization idea. In particular the simulation on bone external shape has been accomplished, thus the simulation on bone growth can become possible.

关 键 词：骨自优化理论 生长过程 模拟 椎体 拓扑优化 

分 类 号：R68[医药卫生—骨科学] R318.01[医药卫生—外科学]