Tsirakos D, Baltzopoulos V, Bartlett R
Manchester Metropolitan University, Crewe and Alsager Faculty, Department of Exercise and Sport Science, England.
Crit Rev Biomed Eng. 1997;25(4-5):371-407. doi: 10.1615/critrevbiomedeng.v25.i4-5.20.
This paper is a review of the optimization techniques used for the solution of the force-sharing problem in biomechanics; that is, the distribution of the net joint moment to the force generating structures such as muscles and ligaments. The solution to this problem is achieved by the minimization (or maximization) of an objective function that includes the design variable (usually muscle forces) that are subject to certain constraints, and it is generally related to physiological or mechanical properties such as muscle stress, maximum force or moment, activation level, etc. The usual constraints require the sum of the exerted moments to be equal to the net joint moment and certain boundary conditions restrict the force solutions within physiologically acceptable limits. Linear optimization (objective and constraint functions are both linear relationships) has limited capabilities for the solution of the force sharing problem, although the use of appropriate constraints and physiologically realistic boundary conditions can improve the solution and lead to reasonable and functionally acceptable muscle force predictions. Nonlinear optimization provides more physiologically acceptable results, especially when the criteria used are related to the dynamics of the movement (e.g., instantaneous maximum force derived from muscle modeling based on length and velocity histories). The evaluation of predicted forces can be performed using direct measurements of forces (usually in animals), relationship with EMG patterns, comparisons with forces obtained from optimized forward dynamics, and by evaluating the results using analytical solutions of the optimal problem to highlight muscle synergism for example. Global objective functions are more restricting compared to local ones that are related to the specific objective of the movement at its different phases (e.g., maximize speed or minimize pain). In complex dynamic activities multiobjective optimization is likely to produce more realistic results.
本文综述了用于解决生物力学中力分配问题的优化技术；即净关节力矩在诸如肌肉和韧带等力产生结构上的分布。通过最小化（或最大化）一个目标函数来解决这个问题，该目标函数包含受某些约束的设计变量（通常是肌肉力），并且通常与生理或力学特性相关，如肌肉应力、最大力或力矩、激活水平等。通常的约束要求施加力矩的总和等于净关节力矩，并且某些边界条件将力的解限制在生理可接受的范围内。线性优化（目标函数和约束函数都是线性关系）在解决力分配问题方面能力有限，尽管使用适当的约束和生理现实的边界条件可以改进解并得出合理且功能上可接受的肌肉力预测。非线性优化提供了更符合生理的结果，特别是当所使用的标准与运动动力学相关时（例如，基于长度和速度历史从肌肉建模得出的瞬时最大力）。可以使用力的直接测量（通常在动物中）、与肌电图模式的关系、与从优化的正向动力学获得的力进行比较以及通过使用最优问题的解析解评估结果来突出肌肉协同作用等方式来评估预测的力。与与运动不同阶段的特定目标相关的局部目标函数相比，全局目标函数的限制更多（例如，最大化速度或最小化疼痛）。在复杂的动态活动中，多目标优化可能会产生更现实的结果。
