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Multi-channel intramuscular and surface EMG decomposition by convolutive blind source separation

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Journal of Neural Engineering
Authors:
Francesco Negro at University of Brescia
Francesco Negro
Silvia Muceli at Chalmers University of Technology
Silvia Muceli
Margherita Castronovo at Imperial College London
Margherita Castronovo
Ales Holobar at University of Maribor
Ales Holobar
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Abstract and Figures

Objective. The study of motor unit behavior has been classically performed by selective recording systems of muscle electrical activity (EMG signals) and decomposition algorithms able to discriminate between individual motor unit action potentials from multi-unit signals. In this study, we provide a general framework for the decomposition of multi-channel intramuscular and surface EMG signals and we extensively validate this approach with experimental recordings. Approach. First, we describe the conditions under which the assumptions of the convolutive blind separation model are satisfied. Second, we propose an approach of convolutive sphering of the observations followed by an iterative extraction of the sources. This approach is then validated using intramuscular signals recorded by novel multi-channel thin-film electrodes on the Abductor Digiti Minimi of the hand and Tibilias Anterior muscles, as well as on high-density surface EMG signals recorded by electrode grids on the First Dorsal Interosseous muscle. The validation was based on the comparison with the gold standard of manual decomposition (for intramuscular recordings) and on the two-source method (for comparison of intramuscular and surface EMG recordings) for the three human muscles and contraction forces of up to 90% MVC. Main results. The average number of common sources identified for the validation was 14 ± 7 (averaged across all trials and subjects and all comparisons), with a rate of agreement in their discharge timings of 92.8 ± 3.2%. The average Decomposability Index, calculated on the automatic decomposed signals, was 16.0 ± 2.2 (7.3–44.1). For comparison, the same index calculated on the manual decomposed signals was 15.0 ± 3.0 (6.3–76.6). Significance. These results show that the method provides a solid framework for the decomposition of multi-channel invasive and non-invasive EMG signals that allows the study of the behavior of a large number of concurrently active motor units.
Representative example of the working principles of the algorithm on a synthetic signal. Three synthetic sources were mixed in three observations. The synthetic MUAP shapes had a duration of 9 samples. Therefore, for clarity and graphical purposes, we show the steps of the algorithm with an extension factor equal to 9. However, we performed the calculation using an actual extension factor of 30 (>3 sources x 9 samples). (I) Raw synthetic EMG mixture. (II) Extended EMG measurements (left) and the corresponding correlation matrix (right). (III) Whitened extended EMG measurements (left) and corresponding correlation matrix (approximately diagonal) (right). (IV) Projection vector (left) and the estimated source (right) after the first step of the fixed point algorithm. (V) Projection vector (left) and the estimated source (right) after the last step of the fixed point algorithm. (VI) Improvement of the estimation (see figure 3 for details) and calculation of the SIL measure. The SIL is a normalized measure of the distance between the clusters of the detected points (c1) and the cluster of the noise values (c2).
Representative example of the working principles of the algorithm on a synthetic signal. Three synthetic sources were mixed in three observations. The synthetic MUAP shapes had a duration of 9 samples. Therefore, for clarity and graphical purposes, we show the steps of the algorithm with an extension factor equal to 9. However, we performed the calculation using an actual extension factor of 30 (>3 sources x 9 samples). (I) Raw synthetic EMG mixture. (II) Extended EMG measurements (left) and the corresponding correlation matrix (right). (III) Whitened extended EMG measurements (left) and corresponding correlation matrix (approximately diagonal) (right). (IV) Projection vector (left) and the estimated source (right) after the first step of the fixed point algorithm. (V) Projection vector (left) and the estimated source (right) after the last step of the fixed point algorithm. (VI) Improvement of the estimation (see figure 3 for details) and calculation of the SIL measure. The SIL is a normalized measure of the distance between the clusters of the detected points (c1) and the cluster of the noise values (c2).
… 
Representative example of the automatic identification of one motor unit spike train using the proposed algorithm (up to the first iteration cycle). At each iteration, a selected contrast function (1/3x³ in this case) applied to the estimated source (estimation of non-gaussianity) is computed. The convergence is reached when the measure of non-gaussianity does not vary with respect to the previous iteration, up to a tolerance (tolx) that was fixed to 10⁻⁴ in this example. A peak detection approach and K-means classification is then applied for a first estimate of the instantaneous discharge pattern of the motor unit. The full method proposed in this study also includes a second iteration cycle, whose effect is not shown here.
Representative example of the automatic identification of one motor unit spike train using the proposed algorithm (up to the first iteration cycle). At each iteration, a selected contrast function (1/3x³ in this case) applied to the estimated source (estimation of non-gaussianity) is computed. The convergence is reached when the measure of non-gaussianity does not vary with respect to the previous iteration, up to a tolerance (tolx) that was fixed to 10⁻⁴ in this example. A peak detection approach and K-means classification is then applied for a first estimate of the instantaneous discharge pattern of the motor unit. The full method proposed in this study also includes a second iteration cycle, whose effect is not shown here.
… 
Representative example of the application of the Gram–Schmidt orthogonalization procedure used to increase the number of estimated sources. The same surface EMG signal (muscle TA, contraction force 20% MVC) was decomposed without (13 motor unit spike trains extracted, blue spikes) and with the proposed orthogonalization (all 33 spike trains shown; the gray spikes are those extracted only with orthogonalization). With orthogonalization, a total of 33 sources, of which 13 corresponding to those extracted without orthogonalization, were extracted.
Representative example of the application of the Gram–Schmidt orthogonalization procedure used to increase the number of estimated sources. The same surface EMG signal (muscle TA, contraction force 20% MVC) was decomposed without (13 motor unit spike trains extracted, blue spikes) and with the proposed orthogonalization (all 33 spike trains shown; the gray spikes are those extracted only with orthogonalization). With orthogonalization, a total of 33 sources, of which 13 corresponding to those extracted without orthogonalization, were extracted.
… 
Example of the application of the second iterative procedure for improving the source estimation accuracy. At each iteration, the new projection vector (see step 5 in the pseudo code of the full algorithm in Methods) and the estimated innervation pulse train are shown. (A) Estimated discharge times (orange circles) extracted from the innervation pulse train at the last iteration of the fixed point algorithm. The comparison with the manual decomposition revealed several missed firings (red circles). (B) Estimated discharge times after the first iteration of the second iterative cycle. (C) Estimated discharge times at the last (third in this case) iteration of the second iterative cycle. The rate of agreement (RoA) for the extracted motor unit spike train improved from 80.5% to 100% with just three iterations.
Example of the application of the second iterative procedure for improving the source estimation accuracy. At each iteration, the new projection vector (see step 5 in the pseudo code of the full algorithm in Methods) and the estimated innervation pulse train are shown. (A) Estimated discharge times (orange circles) extracted from the innervation pulse train at the last iteration of the fixed point algorithm. The comparison with the manual decomposition revealed several missed firings (red circles). (B) Estimated discharge times after the first iteration of the second iterative cycle. (C) Estimated discharge times at the last (third in this case) iteration of the second iterative cycle. The rate of agreement (RoA) for the extracted motor unit spike train improved from 80.5% to 100% with just three iterations.
… 
Example of validation performed on one set of thin-film EMG signals recorded from the TA muscle decomposed manually and automatically with the proposed method. For each extracted motor unit spike train, the instantaneous discharge rate is shown for the automatic decomposition (circles) and the manual decomposition (crosses). The mismatches are in red. pps: pulses per second.
+5
Example of validation performed on one set of thin-film EMG signals recorded from the TA muscle decomposed manually and automatically with the proposed method. For each extracted motor unit spike train, the instantaneous discharge rate is shown for the automatic decomposition (circles) and the manual decomposition (crosses). The mismatches are in red. pps: pulses per second.
… 
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Multi-channel intramuscular and surface
EMG decomposition by convolutive blind
source separation
Francesco Negro
1
, Silvia Muceli
1
, Anna Margherita Castronovo
1
,
Ales Holobar
2
and Dario Farina
1
1
Institute of Neurorehabilitation Systems, Bernstein Focus Neurotechnology Göttingen, Bernstein Center
for Computational Neuroscience, University Medical Center Göttingen, Georg-August University of
Göttingen, Göttingen, Germany
2
Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia
E-mail: dario.farina@bccn.uni-goettingen.de
Received 24 July 2015, revised 1 December 2015
Accepted for publication 27 January 2016
Published 29 February 2016
Abstract
Objective. The study of motor unit behavior has been classically performed by selective
recording systems of muscle electrical activity (EMG signals)and decomposition algorithms
able to discriminate between individual motor unit action potentials from multi-unit signals. In
this study, we provide a general framework for the decomposition of multi-channel
intramuscular and surface EMG signals and we extensively validate this approach with
experimental recordings. Approach. First, we describe the conditions under which the
assumptions of the convolutive blind separation model are satisfied. Second, we propose an
approach of convolutive sphering of the observations followed by an iterative extraction of the
sources. This approach is then validated using intramuscular signals recorded by novel multi-
channel thin-film electrodes on the Abductor Digiti Minimi of the hand and Tibilias Anterior
muscles, as well as on high-density surface EMG signals recorded by electrode grids on the First
Dorsal Interosseous muscle. The validation was based on the comparison with the gold standard
of manual decomposition (for intramuscular recordings)and on the two-source method (for
comparison of intramuscular and surface EMG recordings)for the three human muscles and
contraction forces of up to 90% MVC. Main results. The average number of common sources
identified for the validation was 14±7(averaged across all trials and subjects and all
comparisons), with a rate of agreement in their discharge timings of 92.8±3.2%. The average
Decomposability Index, calculated on the automatic decomposed signals, was 16.0±2.2
(7.3–44.1). For comparison, the same index calculated on the manual decomposed signals was
15.0±3.0 (6.3–76.6).Significance. These results show that the method provides a solid
framework for the decomposition of multi-channel invasive and non-invasive EMG signals that
allows the study of the behavior of a large number of concurrently active motor units.
Keywords: EMG, motor unit, motor neuron, decomposition, blind source separation
(Some figures may appear in colour only in the online journal)
Introduction
Since the pioneering work of Adrian and Bronk (Adrian and
Bronk 1929), the recording of the discharge timings of motor
units during voluntary contractions has provided a
fundamental knowledge to our understanding of human
movement (Heckman and Enoka 2004,2012). The access to
motor units can occur via recording of the muscle fiber action
potentials since the neuro-muscular junction is a highly reli-
able synaptic connection (Enoka 2008). Each discharge of a
Journal of Neural Engineering
J. Neural Eng. 13 (2016)026027 (17pp)doi:10.1088/1741-2560/13/2/026027
1741-2560/16/026027+17$33.00 © 2016 IOP Publishing Ltd Printed in the UK1
... HD-sEMG signals recorded during the experimental tasks were offline decomposed to identify the activity of individual MUs using a convolutive blind source separation algorithm (Negro et al., 2016). To ensure high-quality data, spike trains with a silhouette value (SIL) below 0.9 were automatically discarded (Holobar et al., 2014;Negro et al., 2016). ...
... HD-sEMG signals recorded during the experimental tasks were offline decomposed to identify the activity of individual MUs using a convolutive blind source separation algorithm (Negro et al., 2016). To ensure high-quality data, spike trains with a silhouette value (SIL) below 0.9 were automatically discarded (Holobar et al., 2014;Negro et al., 2016). The decomposed spike trains were then manually reviewed to identify and correct errors. ...
... Following these procedures, additional quality control criteria were applied. MUs were excluded if their SIL was below 0.9, their firing duration was less than 50% of the task time, or their instantaneous firing rate had a standard deviation exceeding 20 Hz (Del Vecchio et al., 2020;Negro et al., 2016). Decomposition and manual editing were conducted using the MUedit MATLAB application (Avrillon et al., 2024a). ...
Projection of Cortical Beta Band Oscillations to a Motor Neuron Pool Across the Full Range of Recruitment
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Cortical beta band oscillations (13 - 30 Hz) are associated with sensorimotor control, but their precise role remains unclear. Evidence suggests that for low-threshold motor neurons, these oscillations are conveyed to muscles via the fastest corticospinal fibers. However, their transmission to motor neurons of different sizes may vary due to differences in the relative strength of corticospinal and reticulospinal projections across the motor neuron pool. Consequently, it remains uncertain whether corticospinal beta transmission follows similar pathways and maintains consistent strength across the entire motor neuron pool. To investigate this, we examined beta activity in motor neurons innervating the tibialis anterior muscle across the full range of recruitment thresholds in a study involving 12 participants of both sexes. We characterized beta activity at both the cortical and motor unit levels while participants performed contractions from mild to submaximal levels. Corticomuscular coherence remained unchanged across contraction forces after normalizing for the net motor unit spike rate, suggesting that beta oscillations are transmitted with uniform strength to motor neurons, regardless of size. To further explore beta transmission, we estimated corticospinal delays using the cumulant density function, identifying peak correlations between cortical and muscular activity. Once compensated for variable peripheral axonal propagation delay across motor neurons, the corticospinal delay remained stable, and its value (approximately 14 ms) indicated projections through the fastest corticospinal fibers for all motor neurons. These findings demonstrate that corticospinal beta band transmission is determined by the fastest pathway connecting in the corticospinal tract, projecting uniformly across the entire motor neuron pool.
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... Specific details regarding analysis and statistical methodologies can be found below. Briefly, HDsEMG was decomposed into individual MU spike trains using convolutive blind source separation and successive sparse J Physiol 0.0 deflation improvements (Martinez-Valdes et al., 2017;Negro et al., 2016) and fit with support vector regression (Beauchamp, Khurram et al., 2022). MU discharge profiles were analysed as detailed below. ...
... Following collection, each channel of surface EMG was visually inspected to remove channels with substantial artifacts, noise or saturation of the A/D board. The remaining EMG channels were decomposed into individual MU spike trains using convolutive blind source separation and successive sparse deflation improvements (Martinez-Valdes et al., 2017;Negro et al., 2016). The silhouette threshold for decomposition was set to 0.87. ...
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