A Quantitative Evaluation of the Frequency-Response Characteristics of Active Human Skeletal Muscle In Vivo

Abstract

This paper describes an investigation of the frequency-response characteristics of active human skeletal muscle in vivo over the frequency range 1 Hz to 15 Hz. The applied force, forearm position, and surface electromyograms (from biceps, triceps, and brachioradialis) were recorded simultaneously in four normal adult male subjects for small oscillations of the forearm about a mean position of 90 deg flexion. Two modes of oscillatory behavior are discussed: externally forced oscillations under constant muscle force and voluntary oscillations against an elastic resistance. The observed amplitude and phase relations are presented herein and are compared to the response predicted by a simple model for neuromuscular dynamics. It appears that the small amplitude frequency response of normal skeletal muscle in vivo can be represented by a second order model. The main muscle parameters of this model are a muscular stiffness K, two time constants τ1 and τ2 associated with contraction dynamics, and a time delay τ: typical values of these parameters at moderate contraction levels (approximately 20 percent of maximum voluntary effort) are K = 100 N · m/rad, τ1 and τ2 = 50 ms, and τ = 10 ms. Reflex feedback under forced-oscillation conditions was also examined and may be characterized by a gain parameter (ΔE/Δθ), the ratio of the surface EMG amplitude to the angular displacement of the forearm, and the phase by which the EMG leads muscle stretch. The reflex EMG is observed to lead muscle stretch at all frequencies between 1 Hz and 15 Hz. The muscle stiffness K and the reflex gain parameter (ΔE/Δθ) are approximately proportional to the average force of contraction.