Wu J Z, Herzog W
Faculty of Kinesiology, Department of Mechanical Engineering, The University of Calgary, Alberta, Canada.
J Biomech. 1999 Aug;32(8):837-48. doi: 10.1016/s0021-9290(99)00057-3.
Despite its overwhelming acceptance in muscle research, the cross-bridge theory does not account for all phenomena observed during muscular contractions. A phenomenon which has received much attention in the biomechanics literature, but has evaded convincing explanation and is not accounted for in the formulation of the classic cross-bridge theory, is the persistent aftereffects of muscular length changes on force production. For example, following muscle shortening, the isometric force of a muscle is depressed for a long time period ( > 5 s) compared to the corresponding isometric force following no length change. In the present study, the classic cross-bridge model was modified in two ways in an attempt to account for the force depressions following muscle shortening. First, the steady-state force depressions following shortening were described by a single scalar variable: the work performed by the muscle during shortening; and second, the dynamic, history-dependent cross-bridge properties were described using a fading memory function. The proposed model was developed and tested for shortening of the cat soleus at constant speeds ranging from 4 to 32 mm/s, for shortening at changing speeds, and for shortening of different magnitudes ranging from 2 to 10 mm. The history-dependent forces during shortening and the steady-state force depressions following shortening were well captured with the modified cross-bridge model. The present model contains two mathematically simple adaptations to the classic cross-bridge model, and is the first such model to account for the long-lasting force depressions following muscle shortening using a single scalar variable.
尽管横桥理论在肌肉研究中被广泛接受，但它并不能解释肌肉收缩过程中观察到的所有现象。在生物力学文献中备受关注但尚未得到令人信服的解释且在经典横桥理论的构建中未被考虑的一个现象是，肌肉长度变化对方力产生的持续后效应。例如，在肌肉缩短后，与无长度变化后的相应等长力相比，肌肉的等长力会在很长一段时间（>5秒）内降低。在本研究中，对经典横桥模型进行了两方面的修改，试图解释肌肉缩短后的力降低现象。首先，缩短后的稳态力降低由一个单一标量变量描述：肌肉在缩短过程中所做的功；其次，使用衰退记忆函数描述动态的、依赖历史的横桥特性。针对猫比目鱼肌以4至32毫米/秒的恒定速度缩短、以变化速度缩短以及2至10毫米范围内不同幅度的缩短情况，开发并测试了所提出的模型。缩短过程中依赖历史的力以及缩短后的稳态力降低情况都能被修改后的横桥模型很好地捕捉。本模型在数学上对经典横桥模型进行了两个简单的调整，并且是第一个使用单一标量变量来解释肌肉缩短后持久力降低的此类模型。
