EMG oscillator model-based energy kernel method for characterizing muscle intrinsic property under isometric contraction

This paper presents a new method for estimating the isometric contraction force and the characterization of muscle’s intrinsic property. The method, called the energy kernel method, starts with converting the electromyography (EMG) signal into planar phase portraits, on which the elliptic distribution of the state points is named as the energy kernel, while that formed by the noise signal is called the noise kernel. Based on such stochastic features of the phase portraits, we approximate the EMG signal within a rectangular window as a harmonic oscillator (EMG oscillator). The study establishes the relationship between the energy of control signal (EMG) and that of output signal (force/power), and a characteristic energy is proposed to estimate the muscle force. On the other hand, the natural frequencies of the noise and the EMG signal can be attained with the energy kernel and noise kernel. In this way, the direct signal–noise recognition and separation can be accomplished. The results show that the representativeness of the characteristic energy toward the force is satisfactory, and the method is very robust since it combines the advantages of both RMS and MPF. Moreover, the natural frequency of the EMG oscillator is not governed by the MU firing rate of a specific muscle, indicating that this frequency correlates with the intrinsic property of muscle. The physical meanings of the model provide new insights into the understanding of EMG.