van Soest A J, Haenen Wouter P, Rozendaal Leonard A
Faculty of Human Movement Sciences and Institute of Fundamental and Clinical Human Movement Sciences, Free University, van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands.
Biol Cybern. 2003 Apr;88(4):293-301. doi: 10.1007/s00422-002-0382-6.
The aim of this study is to assess the contribution of cocontraction and spindle feedback to local stability during bipedal stance. To that aim, an existing nonlinear state space model of the human musculoskeletal system is linearized in a reference equilibrium state. The maximal real part of the eigenvalues of the linearized system matrix A and the low-frequency joint stiffness are used as a measure of local stability. Muscle properties, as represented in a Hill-type muscle model, are shown to improve the behavior, the improvement being larger at high cocontraction. However, even at maximal cocontraction the low-frequency joint stiffness generated by the muscle properties is insufficient to yield a locally stable system. It follows that feedback is necessary to ensure local stability. In this study, the potential contribution of spindle feedback is investigated by optimizing the feedback gains for contractile element length and velocity for each muscle. It is found that in the case of time-delayed negative feedback, it is impossible to stabilize the system on the basis of spindle feedback. When positive time-delayed feedback is allowed, a barely stable system is obtained. When the time delays are removed, the feedback gains can be chosen such that a locally stable system is obtained, indicating the limitations imposed by the presence of time delays. Finally, it is shown that for small perturbations the response of the linear system to an arbitrary perturbation is similar to that of the nonlinear system, indicating the validity of the approach used. It is concluded that the combination of muscle properties and time-delayed spindle feedback is insufficient to obtain a system with reasonable local stability.
本研究的目的是评估双足站立期间协同收缩和肌梭反馈对局部稳定性的贡献。为此，将现有的人体肌肉骨骼系统非线性状态空间模型在参考平衡状态下进行线性化。线性化系统矩阵A的特征值的最大实部和低频关节刚度用作局部稳定性的度量。如希尔型肌肉模型所表示的肌肉特性被证明可以改善行为，在高协同收缩时改善更大。然而，即使在最大协同收缩时，由肌肉特性产生的低频关节刚度也不足以产生局部稳定的系统。因此，反馈对于确保局部稳定性是必要的。在本研究中，通过优化每块肌肉收缩元件长度和速度的反馈增益来研究肌梭反馈的潜在贡献。研究发现，在存在时间延迟的负反馈情况下，不可能基于肌梭反馈使系统稳定。当允许正的时间延迟反馈时，可获得勉强稳定的系统。当去除时间延迟时，可以选择反馈增益以获得局部稳定的系统，这表明了时间延迟的存在所带来的限制。最后，结果表明，对于小扰动，线性系统对任意扰动的响应与非线性系统相似，这表明所采用方法的有效性。结论是，肌肉特性和时间延迟的肌梭反馈的组合不足以获得具有合理局部稳定性的系统。
