Herzog W, Binding P
Faculty of Physical Education and Science, University of Calgary, Alberta, Canada.
Math Biosci. 1992 Oct;111(2):217-29. doi: 10.1016/0025-5564(92)90071-4.
Optimization theory is used more often than any other method to predict individual muscle forces in human movement. One of the limitations frequently associated with optimization algorithms based on efficiency criteria is that they are thought to not provide solutions containing antagonistic muscular forces; however, it is well known that such forces exist. Since analytical solutions of nonlinear optimization algorithms involving multi-degree-of-freedom models containing multijoint muscles are not available, antagonistic behavior in such models is not well understood. The purpose of this investigation was to study antagonistic behavior of muscles analytically, using a three-degree-of-freedom model containing six one-joint and four two-joint muscles. We found that there is a set of general solutions for a nonlinear optimal design based on a minimal cost stress function that requires antagonistic muscular force to reach the optimal solution. This result depends on a system description involving multijoint muscles and contradicts earlier claims made in the biomechanics, physiology, and motor learning literature that consider antagonistic muscular activities inefficient.
优化理论比任何其他方法都更常用于预测人体运动中单个肌肉的力量。基于效率标准的优化算法经常出现的一个局限性是，人们认为它们无法提供包含对抗性肌肉力量的解决方案；然而，众所周知，这种力量是存在的。由于涉及包含多关节肌肉的多自由度模型的非线性优化算法的解析解不可用，此类模型中的对抗性行为尚未得到很好的理解。本研究的目的是使用一个包含六块单关节肌肉和四块双关节肌肉的三自由度模型，对肌肉的对抗性行为进行分析研究。我们发现，基于最小成本应力函数的非线性最优设计存在一组通用解，该函数要求对抗性肌肉力量达到最优解。这一结果取决于涉及多关节肌肉的系统描述，并且与生物力学、生理学和运动学习文献中早期提出的认为对抗性肌肉活动效率低下的观点相矛盾。
