Fyhrie D P, Schaffler M B
Breech Research Laboratory, Bone and Joint Center, Henry Ford Hospital, Detroit, MI 48202.
J Biomech. 1995 Feb;28(2):135-46. doi: 10.1016/0021-9290(94)00059-d.
A phenomenological theory of bone remodeling was developed with improved spatial stability compared to some of the more standard formulations. The improved stability was created by changing the nature of the remodeling differential equation to have an exponential character. As a result, the theoretical predictions are consistent with the experimental observation that changes in bone density during disuse, after hip surgery, during growth and during aging are all consistent with an exponential dependence of density on time. The new theory and the standard theory were both used to model the time course of bone changes in two animal models of bone loss during disuse. The new theory was better able to model the results of the experiments than the standard theory. The basic continuum theory underlying the remodeling theory was presented in some detail. This presentation was used to motivate the development of the new theory, as the standard theories can predict non-smooth distributions of bone density rather than the expected smooth distributions. It was shown that these non-smooth distributions are a violation of the continuum assumption, one of the bases for the theory of finite element stress analysis. The new model's stability was investigated using example problems and shown to be improved compared to the standard model.
与一些更标准的公式相比，我们开发了一种具有更高空间稳定性的骨重塑现象学理论。通过改变重塑微分方程的性质使其具有指数特征，从而实现了稳定性的提升。因此，理论预测与实验观察结果一致，即在废用、髋关节手术后、生长过程和衰老过程中，骨密度的变化均符合密度对时间的指数依赖性。新理论和标准理论都被用于模拟两种废用性骨质流失动物模型中骨变化的时间进程。与标准理论相比，新理论能够更好地模拟实验结果。详细介绍了重塑理论背后的基本连续介质理论。之所以进行此介绍，是为了推动新理论的发展，因为标准理论会预测出骨密度的非平滑分布，而不是预期的平滑分布。结果表明，这些非平滑分布违反了连续介质假设，而连续介质假设是有限元应力分析理论的基础之一。通过实例问题研究了新模型的稳定性，结果表明与标准模型相比其稳定性有所提高。
