反演在骨生长方程参数识别中的应用

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.

Bone Growth Equation and Parameters Identification

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.