应变能密度作控制变量的骨干表面再造—理论预测

用应变能密度作控制变量,其改变量作再造动力,在常压下,将骨干抽象成圆柱形筒,进行骨干表面再造的理论预测。推出的控制内外表面移动的非线性微分方程组的解有８ 种类型,对应的压力值和内外表面再造率系数有４５ 种。它包括了Ｃｏｗｉｎ 用应变作控制变量的理论预测的解。尽管模型与实际相比有一定局限性,但仍能与典型的动物试验结果相一致。从而从理论上说明了用应变能密度作控制变量的适应性骨再造的可靠性。

BONE SURFACE REMODELLING IN THE DIAPHYSIS USING STRAIN ENERGY DENSITY AS CONTROLLED VARIABLE: THEORITICAL PREDICTIONS

Theoretical predictions of surface bone remodelling in the diaphysis of a long bone under a constant compressive load are made using strain energy density as controlled variable. The bone is modeled as a hollow circular cylinder. The non linear differential equations governing movement of the periosteal and endosteal surface was deduced. It is shown that there are eight possible types of solutions to the problem. The particular type of response depends upon the magnitude of the applied compressive load and the values of the surface remodelling rate coefficients. For which there are fortyfive different types. Our solution include the solution got by Cowin using strain as controlled variable. Although the limitation of the theoretical model is exit, it can still consist with the typical animal experimental result. So reliability of adaptive bone remodeling using strain energy density as controlled variable was confirmed in the theory.