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反演在骨生长方程参数识别中的应用
引用本文:刘迎曦,张军,赵文志,孙秀珍.反演在骨生长方程参数识别中的应用[J].力学学报,2005,37(6):805-809.
作者姓名:刘迎曦  张军  赵文志  孙秀珍
作者单位:大连理工大学工程力学系,116024
基金项目:国家自然科学基金(10472025) 辽宁省自然科学基金资助项目(20032109).~~
摘    要:基于BFGS算法,根据自行设计的动物实验,得到在不同应力环境中,快速生长期大鼠股骨生 长与重建过程中骨密度实测数据,采用反演数值方法,获取了骨生长方程中随时间变化的 生物参数B和K. 通过正演验证,表明所建立的基于BFGS算法的参数识别方法具有较好的 稳定性和较高的识别精度,能够反演出比较切合实际的生物参数数值. 研究表明,反问 题方法是解决生命现象不可测性和未知性问题的有效手段,把反演方法应用到骨生长与重建 等生命现象的研究中,可确定、修正预设的数学模式,为数值量化骨适应生物模型的建立提 供了一条可行的途径.

关 键 词:骨生长方程  参数识别  动物实验  骨密度  BFGS算法  
文章编号:0459-1879(2005)06-0805-05
收稿时间:2004-07-09
修稿时间:2005-06-10

Bone Growth Equation and Parameters Identification
Liu Yingxi,Zhang Jun,Zhao Wenzhi,Sun Xiuzhen.Bone Growth Equation and Parameters Identification[J].chinese journal of theoretical and applied mechanics,2005,37(6):805-809.
Authors:Liu Yingxi  Zhang Jun  Zhao Wenzhi  Sun Xiuzhen
Institution:1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;2.Department of Orthopaedics, The Second Affiliated Hospital of Dalian Medical University, Dalian 116027, China;3.E.N.T. Department, The Second Affiliated Hospital of Dalian Medical University, Dalian 116027, China
Abstract:This study presented a method to identify the main parameters (B and K) in bone growth and remodeling equation, which was based on the animal experiment of rapid-growing rats in different stress environment. These results were proved to be of good stability and identification precision with the numerical method of BFGS by analysis. It suggested that B and K were variables changing with time and space. The research showed that solving the uncertainty and unknown properties of life phenomenon with inversion theory and method is an effective way. The idea and method used in the research of bone growth and remodeling adaptation and quantification of unknown parameters of bone growth equation in this paper also provided clue and reference to establish human model of bone growth and remodeling.
Keywords:bone growth equation  parameter identification  animal experiment  bone mineral density  algorithm of BFGS
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