Stochastic properties of individual motor unit interspike intervals

Inter-discharge interval distribution of motor unit firing patterns with detection errors

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%.

Statistically rigorous calculations do not support common input and long-term synchronization of motor-unit firings

Over the past four decades, various methods have been implemented to measure synchronization of motor-unit firings. In this work, we provide evidence that prior reports of the existence of universal common inputs to all motoneurons and the presence of long-term synchronization are misleading, because they did not use sufficiently rigorous statistical tests to detect synchronization. We developed a statistically based method (SigMax) for computing synchronization and tested it with data from 17,736 motor-unit pairs containing 1,035,225 firing instances from the first dorsal interosseous and vastus lateralis muscles--a data set one order of magnitude greater than that reported in previous studies. Only firing data, obtained from surface electromyographic signal decomposition with >95% accuracy, were used in the study. The data were not subjectively selected in any manner. Because of the size of our data set and the statistical rigor inherent to SigMax, we have confidence that the synchronization values that we calculated provide an improved estimate of physiologically driven synchronization. Compared with three other commonly used techniques, ours revealed three types of discrepancies that result from failing to use sufficient statistical tests necessary to detect synchronization. 1) On average, the z-score method falsely detected synchronization at 16 separate latencies in each motor-unit pair. 2) The cumulative sum method missed one out of every four synchronization identifications found by SigMax. 3) The common input assumption method identified synchronization from 100% of motor-unit pairs studied. SigMax revealed that only 50% of motor-unit pairs actually manifested synchronization.

Maximum likelihood estimation of motor unit firing pattern statistics

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.

A technique for the detection, decomposition and analysis of the EMG signal

In the present paper we have described a system for acquiring, processing and decomposing EMG signals for the purpose of extracting as many motor unit action potential trains as possible with the greatest level of accuracy. This system consists of 4 main sections. The first section consists of methodologies for signal acquisition and quality verification. Three channels of EMG signals are acquired using a quadripolar needle electrode designed to enhance discrimination among different MUAPs. An automated experiment control system is devised to free the experimenter from the burden of experiment detailed surveillance and bookkeeping; and to allow on-line assessment of the EMG signal quality in terms of decomposition suitability. The second section consists of methodologies for signal sampling and conditioning. The EMG signal is bandpass filtered (between 1 kHz and 10 kHz), sampled and compressed by eliminating parts of the signal under a preset threshold level. The third section consists of a signal decomposition technique where motor unit action potential trains are extracted from the EMG signal using a highly computer assisted interactive algorithm. The algorithm uses a continuously updated template matching routine and firing statistics to identify MUAPs in the EMG signal. The templates of the MUAPs are continuously updated to enable the algorithm to function even when the shape of a specific MUAP undergoes slow variations. The fourth section deals with ways in which to analyze and display the results. The more frequently used representation formats are: (1) display of MUAP wave shapes; (2) impulse trains representing motor unit firings; (3) IPI plots where time interval between successive firings of the same motor unit is plotted vs. time of the muscle contraction; (4) firing rate plots where the estimated time-varying mean firing rate of the detected motor units is plotted vs. time of the muscle contraction. The performance of the system has been tested in terms of: (1) consistency among results obtained by different operators; (2) accuracy evaluated on synthetic EMG signal; (3) indirect measure of accuracy on real EMG signal by comparing results pertaining the same motor unit action potential trains derived by two EMG signals, independently and simultaneously recorded from two different electrodes.

A linear stochastic model of the single motor unit

The production of force and of the electrical signal by an active motor unit is theoretically described. Neural spikes are modelled using the Dirac delta function. Mechanisms for the generation of random impulse trains and the properties of the corresponding stochastic processes are discussed; the "renewal" model is proposed as the most appropriate. The possibility of using a linear model for the systems that produce force and electrical signal in the unit is examined. It is concluded that the linear assumption is justifiable during steady, constant-strength contractions of muscle. This linear stochastic model of the motor unit is used in two subsequent papers to study the muscle force and the electromyogram.

Lumped and population stochastic models of skeletal muscle: implications and predictions

Lumped models of skeletal muscle have been assumed a) in the design of experiments and the interpretation of experimental findings, b) in theoretical studies. In this paper, a population model that takes into account the differing properties and separate (independent) activation of motor units is presented as the most appropriate for muscle. A realistic (for muscle) transformation, population leads to lumped model, resulting in the lumping of motor unit neural signals or system responses, is proposed. On this basis, the possibility of modelling muscle as a single system is examined; and the consequences of treating muscle as a lumped system, in experiments or theoretical studies, are discussed. Also, the advantages of lumping, in models of muscle, are reviewed. Predictions of a computer population model, together with actual recordings from a hand muscle, are used to confirm the results of the analysis.