A model of central commands (CCs) coming to the muscles during limb movements is proposed; it is based on experimental studies of the nonlinear dynamics of muscle contraction and of the parafrontal two-joint arm movements in humans. It is known that such CCs possess powerful hysteresis properties; levels of muscle activation rise within parts of the movement trajectories, where the muscles are actively shortened and overcome the action of an external force, but decrease during muscle stretching by the above force. Basing on an analogy with the classic thermodynamics, a “thermodynamic” model (T-model) is proposed, which allows one to predict the nonlinear functional interdependence of three basic parameters defining the muscle state, namely E (intensity of efferent activity), F (muscle force), and L (muscle length). The T-model includes the time-dependent integration of the equations defining the interrelations between infinitesimal changes of the above parameters, which are assumed to be the exact differentials. By inducing only one additional parameter, the hysteresis weight, the T-model can satisfactorily explain patterns of EMG records observed in real movements of the arm.

中文翻译：

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上肢运动过程中传递到肌肉的中枢指令的“热力学”模型

提出了在肢体运动过程中到达肌肉的中央命令 (CC) 模型；它基于对肌肉收缩的非线性动力学和人类额旁双关节手臂运动的实验研究。众所周知，这种 CC 具有强大的滞后特性；在运动轨迹的某些部分，肌肉激活水平升高，肌肉主动缩短并克服外力的作用，但在上述力的肌肉拉伸过程中降低。基于与经典热力学的类比，提出了一种“热力学”模型（T 模型），它允许人们预测定义肌肉状态的三个基本参数的非线性函数相互依赖性，即 E（传出活动强度）、F （肌肉力量）和 L（肌肉长度）。T 模型包括方程的时间相关积分，这些方程定义了上述参数的无穷小变化之间的相互关系，这些参数被假定为精确的微分。通过仅引入一个附加参数，滞后权重，T 模型可以令人满意地解释在手臂实际运动中观察到的 EMG 记录模式。