Zahalak G I, Pramod R
Exp Brain Res. 1985;58(2):305-17. doi: 10.1007/BF00235312.
The dynamic relations between the surface myoelectric activity in tonically contracting triceps brachii and the forearm rotation (proportional to triceps stretch) were measured by imposing small, sinusoidal, displacement-controlled perturbations on the forearm position. Three normal, adult, male subjects participated in these experiments. The amplitude of the forearm rotation, the driving frequency, and the tonic contraction level were all carefully regulated. The mean rectified triceps EMG (the output) showed a strong harmonic at the driving frequency, and the frequency-response characteristics were computed directly by comparing the amplitude and phase of this harmonic to that of the forearm flexion angle (the input). The (electrical) reflex gain is defined as the amplitude ratio of output to input. The system response was measured from 2 to 18 Hz, at two tonic contraction levels and two forearm rotation amplitudes, about a mean position of 90 degrees forearm flexion. The results show clearly that the system response is nonlinear: the reflex gain decreases with forearm rotation amplitude. (This gain also increases with tonic contraction level for sufficiently low values of the latter variable.) The measured frequency-response characteristics of the system can be modeled approximately as a second-order linear lead filter with a single time delay, followed by a saturating nonlinearity. Both model-independent estimates and least-squares model fitting, yielded values of the time delay of the order of 25 ms, suggesting that a segmental mechanism mediates reflex activity. Simplified calculations and limited measurements are presented to show that a nonlinear system of the type we have identified with constant displacement driving may appear linear under constant torque driving. Our directly-measured frequency-response characteristics differ from those reported by investigators employing random, rather than periodic, driving; possible reasons for these apparent discrepancies are discussed.
通过对前臂位置施加小幅度、正弦波、位移控制的扰动，测量了肱三头肌持续收缩时表面肌电活动与前臂旋转（与肱三头肌伸展成正比）之间的动态关系。三名正常成年男性受试者参与了这些实验。前臂旋转的幅度、驱动频率和持续收缩水平均经过精心调节。肱三头肌肌电的平均整流值（输出）在驱动频率处呈现出强烈的谐波，通过比较该谐波与前臂屈曲角度（输入）的幅度和相位，直接计算出频率响应特性。（电）反射增益定义为输出与输入的幅度比。在大约90度前臂屈曲的平均位置，在两个持续收缩水平和两个前臂旋转幅度下，测量了2至18赫兹的系统响应。结果清楚地表明，系统响应是非线性的：反射增益随前臂旋转幅度减小。（对于后者变量足够低的值，该增益也随持续收缩水平增加。）系统测量的频率响应特性可以近似建模为具有单个时间延迟的二阶线性超前滤波器，随后是饱和非线性。与模型无关的估计和最小二乘模型拟合都得出了约25毫秒的时间延迟值，这表明一种节段机制介导了反射活动。给出了简化计算和有限测量结果，以表明我们所确定的恒定位移驱动类型的非线性系统在恒定扭矩驱动下可能表现为线性。我们直接测量的频率响应特性与采用随机而非周期性驱动的研究人员报告的结果不同；讨论了这些明显差异的可能原因。
