Martin B
Orthopaedic Research Laboratories, University of California at Davis, California, USA.
J Orthop Res. 1995 May;13(3):309-16. doi: 10.1002/jor.1100130303.
This paper assembles current concepts about bone fatigue and osteonal remodeling into a mathematical theory of the repair of fatigue damage and the etiology of stress fracture. The model was used to address three questions. (a) How does the half-life of fatigue damage compare with the duration of the remodeling cycle? (b) Does the porosity associated with the remodeling response contribute to stress fracture? (c) To what extent is a periosteal callus response necessary to augment repair by remodeling? To develop the theory, existing experimental data were used to formulate mathematical relationships between loading, damage, periosteal bone formation, osteonal remodeling, porosity, and elastic modulus. The resulting nonlinear relationships were numerically solved in an iterative fashion using a computer, and the behavior of the model was studied for various loading conditions and values of system parameters. The model adapted to increased loading by increasing remodeling to repair the additional damage and by adding new bone periosteally to reduce strain. However, if too much loading was encountered, the porosity associated with increased remodeling caused the system to become unstable; i.e., damage, porosity, and strain increased at a very high rate and without limit. It is proposed that this phenomenon is the equivalent of a stress fracture and that its biological and mechanical elements are significant in the etiology of stress fractures. Additional experiments must be done to test the model and provide better values for its parameters. However, the instability characteristic is relatively insensitive to changes in model parameters.
本文将当前关于骨疲劳和骨单位重塑的概念整合为一种关于疲劳损伤修复和应力性骨折病因的数学理论。该模型用于解决三个问题。（a）疲劳损伤的半衰期与重塑周期的持续时间相比如何？（b）与重塑反应相关的孔隙率是否会导致应力性骨折？（c）骨膜骨痂反应在多大程度上是通过重塑增强修复所必需的？为了发展该理论，利用现有的实验数据来建立载荷、损伤、骨膜骨形成、骨单位重塑、孔隙率和弹性模量之间的数学关系。使用计算机以迭代方式对所得的非线性关系进行数值求解，并针对各种载荷条件和系统参数值研究模型的行为。该模型通过增加重塑来修复额外损伤，并通过骨膜下添加新骨来降低应变，从而适应增加的载荷。然而，如果遇到过多载荷，与增加的重塑相关的孔隙率会导致系统变得不稳定；即损伤、孔隙率和应变以非常高的速率且无限制地增加。有人提出，这种现象等同于应力性骨折，并且其生物学和力学因素在应力性骨折的病因中具有重要意义。必须进行额外的实验来测试该模型，并为其参数提供更好的值。然而，不稳定性特征对模型参数的变化相对不敏感。
