Lightly damped hand oscillations: acceleration-related feedback and system damping

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Abstract
Acceleration oscillations (physiological tremor or die-away oscillations) of the outstretched hand and surface electromyograms (EMG) from wrist extensors were detected from each of 9 normal subjects. Each lightly damped oscillation (DO) was initiated by a downward tap to the dorsum of the hand. Auto- and cross-spectral analysis of amplitude-demodulated EMG and hand acceleration records gave values of root mean square (rms) amplitude, coherence, and EMG-DO phase. EMG-DO phase was also estimated from average epochs. Average damping ratios were calculated for different DO peaks for DO between 3.5 and 8.25 Hz. All records were obtained with 90-s rest between runs. The average perturbation response was a lightly damped hand oscillation and a highly correlated oscillatory modulation of wrist extensor (Ext) EMG. For DO frequencies between about 4 and 8 Hz, the average demodulated EMG epoch approximated a delayed replica (plus noise) of the average DO epoch, indicating that this feedback signal was transmitted over a single pathway. The frequency of either tremor or DO of the hand decreased with mass loading of the hand in a manner predicted for a 2nd-order system having nearly constant stiffness. Peak Ext EMG led peak wrist flexion by an angle that decreased linearly with increasing frequency, decreasing from about 140.degree. at 4 Hz to about 40.degree. at 8.25 Hz. Phase intercepts of phase-frequency regression lines indicate that the neural feedback signal was related in phase to the negative of acceleration of the DO. The slopes of these regression lines indicate feedback latencies between 40 and 50 ms for 4 sets and about 70 ms for one set of data. Calculated values of phase lead of Ext EMG on wrist flexion were 10-30.degree. smaller than those estimated visually for all but the 1st cycle of the average DO, reflecting a relatively small phase lead during the first cycle of each DO. This small phase lead appeared to result from the combination of a relatively short initial pulse of downward acceleration and a nearly constant feedback latency. This small phase lead was correlated with relatively small damping of the oscillation during the first DO cycle. Variation of the damping ratio with decreasing DO frequency indicates that system damping is determined by combined mechanical and reflex factors. Reflex damping appears to vary partly as a negative function of the angle by which Ext EMG leads wrist flexion, perhaps becoming negative at a phase lead of 40-60.degree. and a DO frequency of about 7-8 Hz. System damping was consistently positive for DO frequencies as high as 8.25 Hz. Since system damping becomes more positive with phase advance, neural feedback may provide an automatic increase in system stability whenever system perturbations increase the amplitude of the resonant oscillations.