Search

EMG filling curve characterizes the EMG filling process and EMG probability density function (PDF) shape change for the entire force range of a muscle.We aim to understand the relation between the physiological and recording variables, and the resulting EMG filling curves. We thereby present an analytical and simulation study to explain how the filling curve patterns relate to specific changes in the motor unit potential (MUP) waveforms and motor unit (MU) firing rates, the two main factors affecting the EMG PDF, but also to recording conditions in terms of noise level. We compare the analytical results with simulated cases verifying a perfect agreement with the analytical model. Finally, we present a set of real EMG filling curves with distinct patterns to explain the information about MUP amplitudes, MU firing rates, and noise level that these patterns provide in the light of the analytical study. Our findings reflect that the filling factor increases when firing rate increases or when newly recruited motor unit have potentials of smaller or equal amplitude than the former ones. On the other hand, the filling factor decreases when newly recruited potentials are larger in amplitude than the previous potentials. Filling curves are shown to be consistent under changes of the MUP waveform, and stretched under MUP amplitude scaling. Our findings also show how additive noise affects the filling curve and can even impede to obtain reliable information from the EMG PDF statistics.

An analytical derivation of the EMG signal's amplitude probability density function (EMG PDF) is presented and used to study how an EMG signal builds-up, or fills, as the degree of muscle contraction increases. The EMG PDF is found to change from a semi-degenerate distribution to a Laplacian-like distribution and finally to a Gaussian-like distribution.We present a measure, the EMG filling factor, to quantify the degree to which an EMG signal has been built-up. This factor is calculated from the ratio of two non-central moments of the rectified EMG signal. The curve of the EMG filling factor as a function of the mean rectified amplitude shows a progressive and mostly linear increase during early recruitment, and saturation is observed when the EMG signal distribution becomes approximately Gaussian. Having presented the analytical tools used to derive the EMG PDF, we demonstrate the usefulness of the EMG filling factor and curve in studies with both simulated signals and real signals obtained from the tibialis anterior muscle of 10 subjects. Both simulated and real EMG filling curves start within the 0.2 to 0.35 range and rapidly rise towards 0.5 (Laplacian) before stabilizing at around 0.637 (Gaussian). Filling curves for the real signals consistently followed this pattern (100% repeatability within trials in 100% of the subjects). The theory of EMG signal filling derived in this work provides (a) an analytically consistent derivation of the EMG PDF as a function of motor unit potentials and motor unit firing patterns; (b) an explanation of the change in the EMG PDF according to degree of muscle contraction; and (c) a way (the EMG filling factor) to quantify the degree to which an EMG signal has been built-up.

Inter-discharge interval (IDI) distribution analysis of motor unit firing patterns is a valuable tool in EMG decomposition and analysis. However, the firing pattern obtained by EMG decomposition may have detection errors: false positives (incorrectly classified firings) and false negatives (missed firings). In this paper, the mathematical derivation of an IDI distribution model that accommodates false positives and false negatives of the detection process is presented. An approximation of the general model to adapt to specific EMG decomposition conditions is also presented. To illustrate the usefulness of the model, the obtained distribution is used to derive the maximum likelihood estimates of the statistics of motor unit firing patterns, the IDI mean and standard deviation, and estimates of the false negative and false positive ratios. Results obtained from simulation experiments and tests with real motor unit firing patterns show an enhanced estimation performance when compared to previously available algorithms. Goodness-of-fit tests applied to estimations for real data corrupted with false positives showed that the model-driven estimations fitted the uncorrupted data better than EFE estimations: 82% versus 52% not rejectable, respectively, when false positives were about 10% of IDIs. With about 5% false positives, the not rejectable estimations were 85% versus 70%.

Estimation of motor unit firing pattern statistics is a valuable method in physiological studies and a key procedure in electromyographic (EMG) decomposition algorithms. However, if any firings within the pattern are undetected or missed during the decomposition process, the estimation procedure can be disrupted. In order to provide an optimal solution, we present a maximum likelihood estimator of EMG firing pattern statistics, taking into account that some firings may be undetected. A model of the inter-discharge interval (IDI) probability density function with missing firings has been employed to derive the maximum likelihood estimator of the mean and standard deviation of the IDIs. Actual calculation of the maximum likelihood solution has been obtained by means of numerical optimization. The proposed estimator has been evaluated and compared to other previously developed algorithms by means of simulation experiments and has been tested on real signals. The new estimator was found to be robust and reliable in diverse conditions: IDI distributions with a high coefficient of variance or considerable skewness. Moreover, the proposed estimator outperforms previous algorithms both in simulated and real conditions.