Wu J Z, Herzog W, Epstein M
Faculty of Kinesiology, Department of Mechanical Engineering, University of Calgary, Alberta, Canada.
J Biomech. 1997 Apr;30(4):371-5. doi: 10.1016/s0021-9290(96)00148-0.
The purpose of this study was to present a solution for the contact of two biphasic cartilage layers which can be used for dynamic loading, is not restricted to predictions over small time periods, and predicts biologically meaningful changes in contact areas over time. The proposed solution was based on the work of Ateshian et al. (1994, J. Biomechanics 27, 1347-1360) who retained the first term of an asymptotic expansion and used an approximate integration which is valid for short time periods. The solution proposed here uses an exact integration, is valid over long time periods, and can be used for increasing loading. The new solution corrects a limitation of the work by Ateshian et al., which manifests itself immediately (i.e. at time t = 0+ s): the rate of change in the contact radius (and therefore, the contact area) is increasing in Ateshian et al.'s solution for a constant force, whereas it is decreasing in the new solution. An increasing rate of change in the contact radius suggests that the contact radius (area) is unbounded, and a steady-state solution cannot be reached, which is physically not correct for the contact of two joint surfaces. In the new solution, the contact radius reaches a steady-state value given sufficient time.
本研究的目的是提出一种用于两个双相软骨层接触的解决方案，该方案可用于动态加载，不限于短时间预测，并能预测接触面积随时间的生物学意义上的变化。所提出的解决方案基于阿泰希安等人（1994年，《生物力学杂志》27卷，第1347 - 1360页）的工作，他们保留了渐近展开的第一项并使用了适用于短时间的近似积分。这里提出的解决方案使用精确积分，在长时间内有效，并且可用于增加加载。新解决方案纠正了阿泰希安等人工作的一个局限性，该局限性在瞬间（即时间t = 0 + 秒时）就表现出来：对于恒定力，在阿泰希安等人的解决方案中接触半径（进而接触面积）的变化率在增加，而在新解决方案中它在减小。接触半径变化率的增加表明接触半径（面积）无界，并且无法达到稳态解，这在物理上对于两个关节表面的接触是不正确的。在新解决方案中，给定足够的时间，接触半径会达到一个稳态值。
