Rectification and non-linear pre-processing of EMG signals for cortico-muscular analysis

https://doi.org/10.1016/S0165-0270(03)00004-9Get rights and content

Abstract

Rectification of the electromyographic (EMG) signal is a commonly used pre-processing procedure that allows detection of significant coherence between EMG and measured cortical signals. However, despite its accepted and wide-spread use, no detailed analysis has been presented to offer insight into the precise function of rectification. We begin this paper with arguments based on single motor unit action potential (AP) trains to demonstrate that rectification effectively enhances the firing rate information of the signal. Enhancement is achieved by shifting the peak of the AP spectrum toward the lower firing rate frequencies, whilst maintaining the firing rate spectra. A similar result is obtained using the analytic envelope of the signal extracted using the Hilbert transform. This argument is extended to simulated EMG signals generated using a published EMG model. Detection of firing rate frequencies is obtained using phase randomised surrogate data, where the original EMG power spectrum exceeds the averaged rectified surrogate spectra at integer multiples of firing rate frequencies. Model simulations demonstrate that this technique accurately determines grouped firing rate frequencies. Extraction of grouped firing rate frequencies prior to coherency analyses may further aid interpretation of significant cortico-muscular coherence findings.

Introduction

A number of recent studies have investigated coherence between cortical signals obtained from electroencephalographic (EEG) or magnetoencephalographic (MEG) measurements and electromyographic (EMG) signals (Salenius et al., 1997, Halliday et al., 1998, Mima and Hallett, 1999a, Mima and Hallett, 1999b, Gross et al., 2000, Marsden et al., 2000, Mima et al., 2000, Ohara et al., 2000). These studies have suggested that coherent synchronization between these separate neural systems reflects an underlying functional coupling or communication between them. However, the precise function and meaning of this cortico-muscular coherence still remains unknown and is widely debated.

A common processing step in all these studies is to rectify the surface EMG prior to subsequent coherence analysis. Whilst this procedure is almost always implemented, the rationale behind this step has received very little attention. The few offered explanations are empirical arguments based upon reasoning applied to single motor unit (MU) trains. These arguments suggest that ‘full wave rectification of the EMG signal provides the temporal pattern of grouped MU firing regardless of its (the action potential (AP)) shape’ (Halliday et al., 1995, Mima and Hallett, 1999a, Mima and Hallett, 1999b). Thus a detailed analysis of the effect of rectification on the power spectrum of the EMG signal could potentially offer useful insight into the interpretation of cortico-muscular coherence.

The assumption in the literature is that rectification enhances timing or firing rate information of the EMG signal. However, it remains speculative that observed peaks in the spectrum of rectified EMG signals are indeed indicative of such information. We investigate this assumption with an analysis of the effect of rectification that is initially based upon single motor unit AP trains (MUAPT's). This analysis is subsequently extended to composite EMG signals containing many MUAPT's. A priori knowledge of the actual timing information would allow an accurate evaluation of whether the rectified EMG does indeed extract this information. In addition, an objective means of detecting firing rate frequencies is required. Thus the approach adopted here is to generate synthetic EMG signals, with known properties and of varying degrees of complexity. We begin by generating single MUAPT's with known firing rates and these are used to evaluate rectification effects. This is then expanded for more realistic simulations containing multiple MU's. The model utilised in this paper is a physiologically based model of the voluntary EMG signal developed by Lowery et al. (2000). The method of surrogate data is introduced to provide an objective threshold for determination of firing rate frequencies.

Section snippets

Analytic methods

The most commonly accepted EMG models represent a MUAPT as a series of unit impulses, or dirac delta functions, δ(t), applied to a linear time-invariant system with impulse response h(t), which describes the MUAP waveform (Agarwal and Gottlieb, 1975, Basmajian and de Luca, 1985). Thus the output of this filter will be the input delta function spike train, δT(t), convolved with h(t). The EMG signal is the summation of the MUAPT's generated by all of the active MU's within the measured muscle

Results

Fig. 5 depicts the power spectrum for the simulated EMG signal in scenario 1, along with the power spectrum of the rectified EMG signal for this simulation. From the figure it may be seen that although the peak at the firing rate frequency in the non-rectified signal's power spectrum is detectable, it would not be possible to easily discriminate this peak from the rest of the signal without a priori knowledge. However, the firing rate frequencies visibly stand out in the power spectrum of the

Discussion

The power spectra of rectified or envelope extracted simulated EMG data exceeds the power spectra of the average rectified or envelope extracted surrogates over certain frequency ranges. Thus for those frequencies, we may reject the null hypothesis that the rectified EMG was generated by a Gaussian linear stochastic process and assume that additional information is contained at those frequencies. A priori knowledge of firing rate distributions indicate that the significant frequencies are

Conclusions

A detailed investigation of the power spectrum of rectified EMG signals was carried out. Model simulations of surface EMG signals with known parameters indicate that the power spectra of rectified EMG signals is magnified at the firing rate frequencies. This is achieved by shifting the peak of the AP spectrum toward the firing rate frequency, whilst leaving the firing spectrum unchanged. Thresholds set using surrogate EMG data generated by phase randomization may be used to reliably extract the

Acknowledgements

The authors are grateful for the financial assistance from the Wellcome Trust, the Medical Research Council of South Africa and from Enterprise Ireland.

References (26)

  • J.V. Basmajian et al.

    Muscles Alive

    (1985)
  • B. Boashash

    Estimating and interpreting the instantaneous frequency of a signal-part 1: Fundamentals

    Proc. IEEE

    (1992)
  • J.C. Coggshall

    Linear models for biological transducers and impulse train spectra: general formulation and review

    Kybernetik

    (1973)
  • Cited by (230)

    • Disrupted cortico-peripheral interactions in motor disorders

      2021, Clinical Neurophysiology
      Citation Excerpt :

      However, unlike strong recommendations of EMG rectification in CKC analysis, it is still under-debate to apply full-wave rectification of the EMG signals (Bourguignon et al., 2019). Rectification could be achieved by taking the absolute value of the signals, EMG rectification could alter the power spectrum of EMG signals towards lower frequencies corresponding to the motor unit firing rate and maintain the firing rate spectra, which could facilitate CMC estimation (Myers et al., 2003). Later analysis argued that EMG rectification impairs the estimation of corticomuscular coherence by influencing the oscillatory input to a single EMG signal or introducing nonlinear distortions to EMG signal and phase spectrum (McClelland et al., 2012; Neto and Christou, 2009).

    View all citing articles on Scopus
    View full text