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Formulation of a mathematical model of bone remodeling taking accont of bone resorption by overload and its application to clinical problems

考虑超负荷骨吸收的骨重建数学模型的建立及其在临床问题中的应用

基本信息

批准号：
11650085
负责人：
TANAKA Eiichi
金额：
$ 2.24万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650085/
关键词：
Bone Remodeling Mathematical Model Biomechanics Overload Bone Resorption バイオメカンクスリモデリング

项目摘要

The phenomenon where bone changes its structure and mechanical property to adapt to mechanical circumstances is called mechanical bone remodeling. In the present study, we formulate a mathematical model of mechanical bone remodeling to describe phenomenological process of bone remodeling with time, and the validity and the accuracy of the proposed model are examined. The incorporation of the model into the finite element code ABAQUS is also discussed. The results obtained from the present study are summarized in the following :1. A mathematical model for uniaxial loading is formulated by representing physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density by n+1 sequential evolution equations with n+1 macroscopic internal state variables.2. This model can quantitatively describe a time dependent process of bone remodeling. The model also shows the independence of loading histories.3. The model was extended to the multiaxial loading case, and is improved to take into account bone resorption by overload.4. The proposed model showed clinically adequate history dependence of bone remodeling : the model may be applicable to problems of rehabilitation and training.5. The model was incorporated into the finite element code ABAQUS to examine the applicability of the model. A single element model is constructed, and the results are compared with the simulation results using only the model. The two results coincide with each other qualitatively.6. The model was also applied to a finite element model of femur. The results showed the optimum structural design of bone trabecula.

骨的结构和力学性质发生变化以适应力学环境的现象称为机械性骨重建。在本研究中，我们制定了一个数学模型的机械骨重建描述骨重建的现象学过程随时间的推移，和所提出的模型的有效性和准确性进行了检查。将该模型纳入有限元程序ABAQUS也进行了讨论。本研究的主要结果如下：1.将从力学刺激到骨密度变化的骨重塑生理信号传递过程用n +1个具有n+1个宏观内部状态变量的序列演化方程表示，建立了单轴加载的数学模型.该模型可以定量描述骨重建的时间依赖性过程。该模型还显示了加载历史的独立性.将模型扩展到多轴加载的情况，并进行了改进，考虑了过载引起的骨吸收.所提出的模型显示了临床上充分的骨重建的历史依赖性：该模型可能适用于康复和训练问题.该模型被纳入有限元程序ABAQUS的适用性进行了检查。建立了单单元模型，并将计算结果与仅使用该模型的仿真结果进行了比较。这两个结果在定性上是一致的.该模型也被应用到股骨的有限元模型。结果表明，骨小梁的结构设计是最佳的。