A muscle architecture model offering control over motor unit fiber density distributions

Masked least-squares averaging in processing of scanning-EMG recordings with multiple discharges

Removing artifacts from nearby motor units is one of the main objectives when processing scanning-EMG recordings. Methods such as median filtering or masked least-squares smoothing (MLSS) can be used to eliminate artifacts in recordings with just one discharge of the motor unit potential (MUP) at each location. However, more effective artifact removal can be achieved if several discharges per position are recorded. In this case, processing usually involves averaging the discharges available at each position and then applying a median filter in the spatial dimension. The main drawback of this approach is that the median filter tends to distort the signal waveform. In this paper, we present a new algorithm that operates on multiple discharges simultaneously and in the spatial dimension. We refer to this algorithm as the multi-masked least-squares smoothing (MMLSS) algorithm: an extension of the MLSS algorithm for the case of multiple discharges. The algorithm is tested using simulated scanning-EMG signals in different recording conditions, i.e., at different levels of muscle contraction and for different numbers of discharges per position. The results demonstrate that the algorithm eliminates artifacts more effectively than any previously available method and does so without distorting the waveform of the signal. Graphical abstract The raw scanning-EMG signal, which can be composed by several discharges of the MU, is processed by the MMLSS algorithm so as to eliminate the artifact interference. Firstly, artifacts are detected for each discharge from the raw signal, obtaining a multi-discharge validity mask that indicates the samples that have been corrupted by artifacts. Secondly, a least-squares smoothing procedure simultaneously operating in the spatial dimension and among the discharges is applied to the raw signal. This second step is performed using only the not contaminated samples according to the validity mask. The resulting MMLSS-processed scanning-EMG signal is clean of artifact interference.

A Comprehensive Mathematical Model of Motor Unit Pool Organization, Surface Electromyography, and Force Generation

Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. Previous publications have focused on thorough analyses of particular aspects of neuromuscular physiology, yet an integration of the various novel findings into a single, comprehensive model is missing. In this article, we provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles, both consolidating and extending the results of previous studies regarding various components of the neuromuscular system. The model comprises motor unit (MU) pool organization, recruitment and rate coding, intracellular action potential generation and the resulting EMG measurements, as well as the generated muscular force during voluntary isometric contractions. Mathematically, it consists of a large number of linear PDEs, ODEs, and various stochastic nonlinear relationships, some of which are solved analytically, others numerically. A parameterization of the electrical and mechanical components of the model is proposed that ensures a physiologically meaningful EMG-force relation in the simulated signals, in particular taking the continuous, size-dependent distribution of MU parameters into account. Moreover, a novel nonlinear transformation of the common drive model input is proposed, which ensures that the model force output equals the desired target force. On a physiological level, this corresponds to adjusting the rate coding model to the force generating capabilities of the simulated muscle, while from a control theoretic point of view, this step is equivalent to an exact linearizing transformation of the controlled neuromuscular system. Finally, an alternative analytical formulation of the EMG model is proposed, which renders the physiological meaning of the model more clear and facilitates a mathematical proof that muscle fibers in this model at no point in time represent a net current source or sink. A consistent description of a complete physiological model as presented here, including thorough justification of model component choices, will facilitate the use of these advanced models in future research. Results of a numerical simulation highlight the model's capability to reproduce many physiological effects observed in experimental measurements, and to produce realistic synthetic data that are useful for the validation of signal processing algorithms.

A masked least-squares smoothing procedure for artifact reduction in scanning-EMG recordings

Scanning-EMG is an electrophysiological technique in which the electrical activity of the motor unit is recorded at multiple points along a corridor crossing the motor unit territory. Correct analysis of the scanning-EMG signal requires prior elimination of interference from nearby motor units. Although the traditional processing based on the median filtering is effective in removing such interference, it distorts the physiological waveform of the scanning-EMG signal. In this study, we describe a new scanning-EMG signal processing algorithm that preserves the physiological signal waveform while effectively removing interference from other motor units. To obtain a cleaned-up version of the scanning signal, the masked least-squares smoothing (MLSS) algorithm recalculates and replaces each sample value of the signal using a least-squares smoothing in the spatial dimension, taking into account the information of only those samples that are not contaminated with activity of other motor units. The performance of the new algorithm with simulated scanning-EMG signals is studied and compared with the performance of the median algorithm and tested with real scanning signals. Results show that the MLSS algorithm distorts the waveform of the scanning-EMG signal much less than the median algorithm (approximately 3.5 dB gain), being at the same time very effective at removing interference components.

Graphical Abstract

Modifying motor unit territory placement in the Fuglevand model

The Fuglevand model is often used to address challenging questions in neurophysiology; however, there are elements of the neuromuscular system unaccounted for in the model. For instance, in some muscles, slow and fast motor units (MUs) tend to reside deep and superficially in the muscle, respectively, necessarily altering the development of surface electromyogram (EMG) power during activation. Thus, the objective of this study was to replace the randomized MU territory (MUT) placement algorithm in the Fuglevand model with an optimized method capable of reflecting these observations. To accomplish this, a weighting term was added to a previously developed optimization algorithm to encourage regionalized MUT placement. The weighting term consequently produced significantly different muscle fibre type content in the deep and superficial portions of the muscle. The relation between simulated EMG and muscle force was found to be significantly affected by regionalization. These changes were specifically a function of EMG power, as force was unaffected by regionalization. These findings suggest that parameterizing MUT regionalization will allow the model to produce a larger variety of EMG-force relations, as is observed physiologically, and could potentially simulate the loss of specific MU types as observed in ageing and clinical populations.

Effect of number of motor units and muscle fibre type on surface electromyogram

Reduction in number of motor units (nMU) and fast fibre ratio (FFR) is associated with disease or atrophy when this is rapid. There is a need to study the effect of nMU and FFR to analyse the association with ageing and disease. This study has developed a mathematical model to investigate the relationship between nMU and FFR on surface electromyogram (sEMG) of the biceps muscles. The model has been validated by comparing the simulation outcomes with experiments comparing the sEMG of physically active younger and older cohort. The results show that there is statistically significant difference between the two groups, and the simulation studies closely model the experimental results. This model can be applied to identify the cause of muscle weakness among the elderly due to factors such as muscle dystrophy or preferential loss of type F muscle fibres.