A new method of simulating surface electromyograms using probability density functions

Abstract

A new method based on probability density functions (inverse Gaussian distributions) to simulate surface electromyograms (sEMGs) was developed for the specific use of the ‘$T_{\mathrm{P}}$ technique’, which discriminates sEMG activity patterns. First, four prototypes with different activity patterns were generated from inverse Gaussian distributions by changing their geometrical parameters, which were derived from actual recorded sEMGs. Then, four simulated sEMGs were produced on the basis of the prototypes. The validity of the simulation method in relation to the $T_{\mathrm{P}}$ technique was statistically examined and verified. The new simulation method will be useful.

Introduction

Skeletal muscle fibers generate multiple action potentials in association with movements that can be measured by surface electromyograms (sEMGs) [1], [2], which are recorded using electrodes placed on the skin and mucosa. sEMGs are commonly employed in basic science research (e.g., physiology and kinesiology) and are often used in clinical settings. Advanced computers and computer software have facilitated sEMG simulation research.

Sophisticated computerized simulation methods have been developed [3], [4], [5], [6]. sEMGs that have been simulated using many available methods generally compile individual action potentials as they occur during biological events [6]. These methods, which were based on simulated action potentials, appear to be suitable for precise computer analysis of biological processes (e.g., activation of individual action potentials from muscle fibers, volume conduction in muscular tissues, and surface electrode recording). Because many parameters are involved and proprietary software is required [3], [4], [5], [6], the conventional methods tend to be cumbersome for simulating sEMGs.

In addition, analysis of actual sEMGs often begins with ‘integration’ of the original action potentials because integration of sEMGs with appropriate time constants is important for measuring various parameters (e.g., duration, mean amplitude, peak amplitude, and integrated area under the curve [3], [4], [5]). Integrated sEMGs can also be used to interpret the activity patterns of the target muscles, but interpretation has been mostly conducted by ‘visual observation’ only. We recently developed a ‘$T_{\mathrm{P}}$ technique’ for the quantitative evaluation of activity patterns observed in integrated sEMGs [7]. The $T_{\mathrm{P}}$ technique is briefly summarized in the following steps: (1) each final cumulative value of an EMG is divided into 10 or 20 equal sections ($10\%,20\%,\dots ,100\%$ or $5\%,10\%,\dots ,100\%$ of the final value); (2) the 10 or 20 sectioned values are allocated serially to a standardized time scale; and (3) the allocated 10 or 20 points are designated on the standardized time scale as $T_{\mathrm{P}}(T_{10},T_{20},\dots ,T_{100}\text{or}{T}_5,T_{10},\dots ,T_{100})$. We used this technique to accurately discriminate sEMG activity patterns that were recorded during different chewing and swallowing behaviors [7], [8], [9]. In a previous paper [7], e.g., we discriminated the activity patterns of the suprahyoid muscles during swallowing of tasted and tasteless foods by the $T_{\mathrm{P}}$ technique. Our previous results generated using this technique [7], [8], [9] suggest that the $T_{\mathrm{P}}$ technique is useful in evaluating actual patterns of sEMGs, but the theoretical basis of the technique has not yet been established. In addition, we need a simulation method that can be modified to the form of distributions. Because probability distribution functions may cause characteristic forms by changing values of the function used (e.g., [10]), in the present study we focused on the properties of probability distribution functions. In the research field of electromyography, Stashuk and Naphan [11] applied the probability distribution functions to indexes to classify motor unit action potentials in simulated signals, and Hamid Nawab et al. [12] improved resolutions in decomposing sEMGs by modifying them into constituent motor unit action potential trains using the probability distribution functions. However, application of the probability distribution functions to simulations of sEMGs has not been reported. In this study, we aimed to establish a simulation method specific for sEMGs to elucidate the theoretical basis for the $T_{\mathrm{P}}$ technique.