Prendergast P J, Taylor D
Mechanical Engineering Department, Trinity College, Dublin, Ireland.
J Biomech. 1994 Aug;27(8):1067-76. doi: 10.1016/0021-9290(94)90223-2.
The adaptation of bones to a change in function has been recognised for many centuries, but only recently have mathematical laws been proposed to describe it. One proposed mathematical law is based on the hypothesis that, after a change in load, the strain in the bone microstructure is regulated to a homeostatic equilibrium. Strain-adaptive remodelling has been used successfully to simulate bone adaptation around orthopaedic implants but the predictive capabilities are constrained because many empirical constants are required in the remodelling law (a reference stimulus, a zone of equilibrium stresses or 'lazy zone' and a parameter transducing macroscopic stresses to a tissue level stimulus). An alternative approach has been proposed. It is that bone adapts to attain an optimal strength by regulating the damage generated in its microstructural elements. The question is raised whether or not a mathematical law to predict the time course of bone adaptation can be derived for damage-adaptive remodelling in a similar way to the mathematical laws based on a strain stimulus. In the present study, the hypotheses required to develop damage-adaptive remodelling laws are proposed and a remodelling law to predict the time course of bone adaptation is derived. It is shown that this is an integral remodelling law which accounts naturally for the stress history to which the tissue has been exposed since formation. A simulation of the adaptive response of a bone diaphysis under a change in torsional load shows that the law gives physically reasonable predictions. The initial remodelling prediction is similar to strain-adaptive remodelling. However, in the later stages of remodelling, the predictions differ from strain-adaptive remodelling in that direct convergence to a homeostatic strain is not predicted. Instead, undershoot (in the case of a reduction in load) and overshoot (in the case of an increase in load) are predicted.
骨骼对功能变化的适应性已被认识了许多世纪，但直到最近才有人提出数学定律来描述它。一种提出的数学定律基于这样的假设：在负荷变化后，骨微结构中的应变会被调节到稳态平衡。应变适应性重塑已成功用于模拟骨科植入物周围的骨适应性，但预测能力受到限制，因为重塑定律中需要许多经验常数（一个参考刺激、一个平衡应力区或“惰性区”以及一个将宏观应力转换为组织水平刺激的参数）。有人提出了另一种方法。即骨骼通过调节其微结构元件中产生的损伤来适应以达到最佳强度。问题是，是否能以类似于基于应变刺激的数学定律的方式，推导出一个预测骨适应性时间进程的数学定律用于损伤适应性重塑。在本研究中，提出了建立损伤适应性重塑定律所需的假设，并推导出了一个预测骨适应性时间进程的重塑定律。结果表明，这是一个积分重塑定律，它自然地考虑了组织自形成以来所经历的应力历史。对骨干在扭转载荷变化下的适应性反应进行的模拟表明，该定律给出了符合物理实际的预测。初始重塑预测与应变适应性重塑相似。然而，在重塑的后期阶段，预测结果与应变适应性重塑不同，因为预测的不是直接收敛到稳态应变。相反，预测会出现下冲（在负荷降低的情况下）和上冲（在负荷增加的情况下）。
