Exact inter-discharge interval distribution of motor unit firing patterns with gamma model

Javier Navallas,Sonia Porta,Armando Malanda

doi:10.1007/s11517-018-01947-y

Javier Navallas, Sonia Porta + Show 1 more

Open Access

https://doi.org/10.1007/s11517-018-01947-y

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Abstract

Inter-discharge interval distribution modeling of the motor unit firing pattern plays an important role in electromyographic decomposition and the statistical analysis of firing patterns. When modeling firing patterns obtained from automatic procedures, false positives and false negatives can be taken into account to enhance performance in estimating firing pattern statistics. Available models of this type, however, are only approximate and use Gaussian distributions, which are not strictly suitable for modeling renewal point processes. In this paper, the theory of point processes is used to derive an exact solution to the distribution when a gamma distribution is used to model the physiological firing pattern. Besides being exact, the solution provides a way to model the skewness of the inter-discharge distribution, and this may make it possible to obtain a better fit with available experimental data. In order to demonstrate potential applications of the model, we use it to obtain a maximum likelihood estimator of firing pattern statistics. Our tests found this estimator to be reliable over a wide range of firing conditions, whether dealing with real or simulated firing patterns, the proposed solution had better agreement than other models.Graphical Model of the MU firing pattern generation and detection: fT,1(τ), IDI PDF of the physiological firing pattern; fT(τ), IDI PDF after modeling undetected firings (false negatives); fS(τ), IDI PDF after modeling classification errors (false positives)

Highlights

Analysis of the motor unit (MU) firing pattern provides invaluable information for EMG analysis [1,2,3,4,5] and the automation and evaluation of EMG decomposition [6,7,8,9,10,11]
When a firing pattern is modeled as a renewal point process, the inter-discharge intervals (IDIs) are independent and distributed following a certain probability density function (PDF)
The gamma distribution allows for some degree of skewness in the IDI PDF, which may enable models based on the gamma distribution to better reflect reality since physiological evidence indicates that the IDI PDF shows low-to-moderate skewness [2, 5, 21]

Summary

Introduction

Analysis of the motor unit (MU) firing pattern provides invaluable information for EMG analysis [1,2,3,4,5] and the automation and evaluation of EMG decomposition [6,7,8,9,10,11]. The firing pattern under certain physiological conditions can be modeled as a renewal point process, and this approach has been demonstrated in physiological studies to be adequate [1,2,3,4, 7]. When a firing pattern is modeled as a renewal point process, the inter-discharge intervals (IDIs) are independent and distributed following a certain probability density function (PDF). Instead of a Gaussian distribution, a more suitable distribution for modeling the physiological IDI PDF is the gamma distribution [4]. This is so because the gamma distribution has nonnegative support, whereas the Gaussian distribution extends into negative values. The gamma distribution allows for some degree of skewness in the IDI PDF, which may enable models based on the gamma distribution to better reflect reality since physiological evidence indicates that the IDI PDF shows low-to-moderate skewness [2, 5, 21]

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