用有限元法耦合反应扩散模型的骨重建和仿生拓扑优化方法研究Study on Bone Remodeling and Bionic Topology Optimization Method by Using Reaction-Diffusion Model Coupled with FEM
买买提明·艾尼
摘要(Abstract)：
本文介绍了用有限元法耦合反应扩散模型的骨重建和仿生拓扑优化理论和方法.首先对骨微结构进行了建模,然后用仿生拓扑优化方法模拟了骨小梁结构的形成过程.对骨骼宏观结构和形状的形成过程也进行了建模并进行了仿生拓扑优化.不同载荷条件下的骨微结构模型在保留体积不同时的仿生拓扑优化结果表明,所有的结果最终都得到小梁结构并在给定的保留体积内趋于稳定,但是小梁尺寸大小有所不同.对于骨骼宏观模型,建立了不同边界条件的模型,用仿生拓扑优化方法模拟了骨骼宏观结构和形状的形成过程,得到了接近股骨、腓骨、脊椎骨、错骨和指骨等实际骨骼形状.
关键词(KeyWords)： 有限元法;反应扩散模型;仿生拓扑优化;小梁结构;骨骼
基金项目(Foundation): 国家自然科学基金资助项目(编号:50775193)
作者(Author): 买买提明·艾尼
参考文献(References)：
- [1]朱兴华,马宗民.带有力学调控系统的各向异性骨再造模型.中国科技论文在线,http://www.paper.edu.cn,2004,03, 03.
- [2]Wolff J.Das gesetz der transformation der knochen[M].(Translated as The Law of Bone Remodeling) Springer,Berlin, 1892.
- [3]Meyer G H.Die architektur der spongiosa,Archief fur den anatomischen und physiologischen Wissenschaften im Medicin[J]. 27,1867,1389-1394.
- [4]Turing A M.The Chemical Basis of Morphogenesis[J].Phil Trans R Soc London B237,1952,37-72.
- [5]Lengyel I,Epstein I R.Modeling of Turing structures in the chlorite-iodidemalonic acid-starch reaction system[J].Science, 1991,251:650-652.
- [6]Ouyang Q,Swinney H L.Transition from a uniform state to hexagonal and striped Turing patterns[J].Nature,1991,352: 610-612
- [7]Kondo S,Asai R.A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus[J].Nature,1995,376:765-768.
- [8]Mullender M G,Huiskes R,Weinans H.Aphysiological approach to the simulation of bone remodeling as a self-organizational control process[J].J Biomechanics,1994,27(11):1389-1394.
- [9]Forst H M.The Utah paradigm of skeletal physiology:an overvief of its insights for bone,cartilage and collagenous tissue organs[J].J Bone Miner Metab,2000,18:305-316.
- [10]Huiskes R,Ruimerman R,van Lenthe G H,et al.Effects of mechanical forces on maintenance and adaptation of form in trabecular bone[J].Nature,2000,405:704-706.
- [11]Tezuka K,Wada Y,Kikuchi M.iBone:A Reaction Diffusion Based Shape Optimization Method[J].Key engineering Materials.2003,243-244:601-606.