Re-Evaluating Electromyogram–Force Relation in Healthy Biceps Brachii Muscles Using Complexity Measures
The objective of this study is to re-evaluate the relation between surface electromyogram (EMG) and muscle contraction torque in biceps brachii (BB) muscles of healthy subjects using two different complexity measures. Ten healthy subjects were recruited and asked to complete a series of elbow flexion tasks following different isometric muscle contraction levels ranging from 10% to 80% of maximum voluntary contraction (MVC) with each increment of 10%. Meanwhile, both the elbow flexion torque and
... flexion torque and surface EMG data from the muscle were recorded. The root mean square (RMS), sample entropy (SampEn) and fuzzy entropy (FuzzyEn) of corresponding EMG data were analyzed for each contraction level, and the relation between EMG and muscle torque was accordingly quantified. The experimental results showed a nonlinear relation between the traditional RMS amplitude of EMG and the muscle torque. By contrast, the FuzzyEn of EMG exhibited an improved linear correlation with the muscle torque than the RMS amplitude of EMG, which indicates its great value in estimating BB muscle strength in a simple and straightforward manner. In addition, the SampEn of EMG was found to be insensitive to the varying muscle torques, almost presenting a flat trend with the increment of muscle force. Such a character of the SampEn implied its potential application as a promising surface EMG biomarker for examining neuromuscular changes while overcoming interference from muscle strength. EMG from biceps muscles showed a curvilinear fashion following the torque increment at different contraction speeds. By contrast, the MDF of signal was found to increase linearly with force, and then it reached a plateau and gradually decreased at large force levels. Karlsson et al.  showed a positive significant linear correlation between the RMS of EMG and the force for three thigh muscles, with very high R-square values ranging from 0.91 to 0.93. In addition, the study by Onishi et al.  suggested a linear correlation between the integrated amplitude of the EMG and the vastus laterals muscle force, but such correlation became very weak when MPF of EMG was used. Bilodeau et al.  found that the RMS amplitude of EMG increased progressively with force in vastus lateralis, rectus femoris and vastus medialis muscles, and the increases in MPF and MDF were also observed. Investigations into the EMG-force relation reported complex and even contradictory findings. For example, some studies suggested a linear relation between the amplitude of EMG and the force in biceps brachii muscle  . However, more researchers considered that the EMG-force relation was more likely to be nonlinear [8, 11] . Furthermore, the research findings were significantly different for different muscles. Some researchers considered that a linear relation appeared mainly in small muscles, such as first dorsal interosseous muscle [13, 14] , and a nonlinear relation emerged in large muscles like quadriceps femoris muscle group [11, 15] . Such the variance might be also caused by underlying motor control mechanisms. Watanabe and Akima  revealed that the neuromuscular activation pattern of individual muscle was one of the main factors altering shape of EMG-force relationship. Specifically, a linear relationship between amplitude of EMG and muscle force up to 50% of MVC is likely to exhibit when the force increment mainly relies on motor unit recruitment. If motor unit firing rate modulation mainly works for further force increase at larger forces, a nonlinear curve can be demonstrated  . Furthermore, the EMG-force relation was found to vary across muscles and individuals, as a typical representative of individual difference in physiological processes. Given such complex findings, recent efforts focus on development of sophisticated methods for modeling muscle force with surface EMG input, including parallel cascade identification (PCI) model  , multi-scale physiology-based model  , blind source separation  and high-order statistics parameters [21, 22] . These methods worked well for force estimation under certain conditions. Considering the nonlinear and non-stationary properties of sEMG, interpreting data with conventional linear time-domain and frequency-domain parameters may unavoidably have limitations. Nonlinear dynamic theory provides an alternative tool for the analysis of EMG signals. There are many analytical parameters for nonlinear complexity analysis, including fractal features  and entropy measures    , which have been frequently applied              . Therein, the approximate entropy (ApEn)  and sample entropy (SampEn)  have been widely used for EMG signal      35, 36] . SampEn is refined on the basis of ApEn, and eliminates the bias and inconsistency for complexity measure. Recently, the fuzzy logic has been introduced into the complexity analysis. Fuzzy entropy (FuzzyEn)  , as a representative, has been widely utilized for analysis [31, 32] . FuzzyEn adopts the fuzzy membership function to replace the Heaviside function for similarity measure, which makes FuzzyEn measure more continuous and smooth. Such advance of FuzzyEn has been confirmed by Chen et al. . With the above-mentioned considerations, this study re-evaluates the EMG-torque relation in biceps brachii (BB) muscles of healthy subjects, from a novel perspective provided by entropy measures. There have been various studies reporting quantitative analyses using various entropy measures, and most of them suggested that the EMG complexity were somehow regulated by the muscle force       . However, few studies aimed to quantify the relation between EMG complexity and muscle force. Therefore, the SampEn and FuzzyEn are both employed in this study to interpret the recorded sEMG data. Characterization of the EMG-torque relation from a novel point of view by parameterizing sEMG signals in the nonlinear complexity domain other than conventional time domain or frequency domain will help to better understand motor control mechanisms underlying muscular activities, and also provide important guidelines for clinical diagnosis and treatment of neuromuscular disorders. Specifically, the EMG-torque relations characterized by both entropy measures along with Entropy 2017, 19, 624 3 of 13 the routine RMS amplitude of EMG signal are likely to exhibit different regulations. The resultant different characters of the EMG-torque relation suggest their specific potentials for biomedical and biomechanical applications.