A masked leastsquares smoothing procedure for artifact reduction in scanningEMG recordings
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Abstract
ScanningEMG 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 scanningEMG 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 scanningEMG signal. In this study, we describe a new scanningEMG signal processing algorithm that preserves the physiological signal waveform while effectively removing interference from other motor units. To obtain a cleanedup version of the scanning signal, the masked leastsquares smoothing (MLSS) algorithm recalculates and replaces each sample value of the signal using a leastsquares 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 scanningEMG 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 scanningEMG signal much less than the median algorithm (approximately 3.5 dB gain), being at the same time very effective at removing interference components.
Keywords
Electromyography ScanningEMG Signal processing Motor unit1 Introduction
Analysis of scanningEMG signals has proved useful not only in the study of neuromuscular pathologies [3, 7, 8, 10, 12, 13, 33] but also, and specially, in the detailed characterization of the anatomical properties of the MU [3, 10, 17, 30, 32, 35]. ScanningEMG signal analysis results in extraction from the signal of several useful descriptive parameters, such as the length of the MU territory [10], the number of MU fractions [31], the temporal delay between fractions [17], and the number of silent zones [31]. More recently, the motor unit profile has been proposed as another way to represent the scanningEMG signal [2].
Reliable information, however, cannot be extracted from a raw scanningEMG signal because such a signal is contaminated with noise and interference (Fig. 1a). There are three different types of noise in scanningEMG recordings. First, there is baseline noise caused by needle or muscle movements [10, 11, 20]; second, there is high frequency noise due to the electronics of the acquisition system; and third, and most troublesome, there is the presence of artifacts deriving from the activation of nearby motor units during MUP recording at each position [10, 11, 20]. The level of interference from these other MUs depends on the level of voluntary contraction exerted by the subject or patient while the recording is being made [21].
Noise characteristics in biomedical signals, which will vary depending on the kind of signal and acquisition system employed, largely determine the suitable signal processing technique to be used [29]. For instance waveletbased methods can be used when dealing with baseline noise [23] or speckle noise [27, 28], and median filter can be used to remove impulsive noise.
Noise and interference elimination has typically two steps in scanningEMG recordings [10, 11, 20]. The first step is to apply a temporal bandpass filter to each of the scanning traces [10, 11, 20] (Fig. 1b). This filter removes the baseline noise in the low frequency range of the spectrum and some of the highfrequency noise from the acquisition system. The second step is to apply a median filter (usually of 3, 5, or 7 points) in the spatial dimension in order to eliminate the artifacts (Fig. 1c). Artifact interference falls within the frequency range of the physiological scanningEMG signal in the temporal dimension, but it does not in the spatial dimension. This is because artifacts are not synchronized with the firing of the MU being tracked, and therefore, they are not consistently repeated in different traces, i.e., in the spatial dimension, they are effectively impulsive noise. This is the reason why the median filter applied in the spatial dimension is so effective at cleaning up scanningEMG signals [11].
The median filter, however, has an important drawback: it considerably distorts the shape of the scanningEMG signal. Peaks of the signal tend to be clipped significantly when the median filter is applied [10, 11, 20]. Peak clipping can be reduced by using a median filter with fewer points, but the fewer the points, the less effectively the artifacts are eliminated [10, 11]. Signal waveform distortion caused by the median filter can induce errors in subsequent analysis of the scanningEMG signal.
In view of the above limitations inherent to the median filter, we suggest an alternative approach should be used for processing scanningEMG signals. We propose a new processing algorithm—we will refer to it as masked leastsquares smoothing (MLSS)—which recalculates and replaces each sample value of the scanning signal using a spatial leastsquares smoothing procedure, taking into account information from only those samples that are not contaminated with artifacts. The algorithm is designed in such a way that it achieves a smooth waveform in the spatial dimension, exploiting the fact that in absence of noise and artifacts, the scanningEMG signal is not expected to present abrupt variations, since the dependence between the recording position and the amplitude of the MUP is smooth [15]. In the present work, the MLSS algorithm is described, and its performance with both simulated and real scanningEMG signals is analyzed and compared with that of the median algorithm.
2 Materials and methods
2.1 Algorithm description
2.1.1 Artifact detection
The first step of the MLSS algorithm is to detect the samples in which the scanningEMG signal is contaminated by artifacts (Fig. 2). Such interference is estimated by obtaining the difference between the N × K scanningEMG signal before, F = {f_{n,k}}, and after Lpoint spatial median filtering, G = {g_{n,k}}, where n and k denote the temporal and spatial location of the sample, and N and K are the number of temporal and spatial samples of the recording.
2.1.2 Spatial leastsquares smoothing
For spacetime positions in which this condition is not satisfied, the highest polynomial order Q that satisfies the condition is chosen.
2.2 Algorithm evaluation
2.2.1 Model of scanningEMG signals
Simulated scanningEMG signals were used to evaluate the performance of the MLSS algorithm. In this section, the simulation model of scanningEMG signals is described.
Muscle and motor unit modeling
Each muscle was created with a circular muscle cross section of 10 mm diameter and was composed of 120 MUs. The crosssectional areas of MU territories were modeled fitting an exponential function [6] between the area of the smallest MU, 1.96 mm^{2}, and the area of the largest MU, 22.48 mm^{2}. MU territories were circular in shape except when constrained by the muscle boundary, in which case the MU territory was cut to fit within the muscle limits, and the radius was regrown so as to keep the territory area unchanged [14, 18, 19]. MU territories were placed within the muscle in such a way that the spatial variance of the overlapping between MU territories within the muscle was minimized [19, 26]. For each MU, muscle fibers were modeled according to a uniform distribution inside the MU territory [5], with a fiber density of 10 fibers/mm^{2}. The length of muscle fibers was 140 mm. The conduction velocity of muscle fibers within the i^{ t h } MU were given by a Gaussian distribution, with a mean conduction velocity modeled by an exponential function [6] between the MU conduction velocity of the smallest MU, 3.25 m/s, and the MU conduction velocity of the largest MU, 6.25 m/s, and with a coefficient of variation 0.03.
Recruitment and firing pattern modeling
The recruitment and firing pattern of each motor unit were modeled according to [5, 6]. The recruitment threshold of the i^{ t h } MU during constant isometric contraction was modeled by an exponential function [5, 6], with a percentage of voluntary contraction (MVC) of full recruitment of 70% [6]. The minimum firing rate was 8 pps (pulses per second), and the firing rate increased linearly with increased strength of voluntary contraction: at a rate of 7 pps for each 10% increase in MVC [5]. The maximum firing rate was 35 pps [5]. The firing train of each MU was modeled as a renewal point process where the interval between discharges followed a Gaussian distribution with a mean that was the inverse of the firing rate, and with a coefficient of variation of 0.15.
ScanningEMG signal modeling
Singlefiber action potentials (SFAPs) were simulated using a line source model [24], and MUPs were generated by the summation of the individual SFAPs [16]. In order to simulate the effect of concentric needle recording [16], MUPs were calculated and averaged for a grid of points over the uptake area [16]. The cannula effect of the concentric needle was also taken into account by simulating and averaging the MUP in the cannula section; the resulting signal was subtracted from the core MUP [16].
The physiological scanningEMG signal was simulated as the sequence of MUPs obtained at each position of the scanning corridor. The scanningEMG signal was simulated from the smallest MU whose territory was traversed by the corridor. The modeled scanning electrode was inserted 30 mm away from the innervation zone. The scanning corridor was located across the plane of muscle cross section, from the bone to the skin, recording a signal every 0.05 mm [30].
In order obtain modeled scanningEMG signals that were realistically noisy, the entire recording procedure was modeled. For each recording position, the EMG signal was calculated as the convolution of the MUPs of all recruited MUs and their corresponding firing trains. Each recording trace was a 30ms duration segment of the complete EMG signal around the corresponding MU firing time. After each trace, a waiting time of 60 ms was emulated in order to model the time a scanning electrode takes to advance to the next recording position.
Baseline noise was modeled as an ARMA process [23] obtained by filtering white Gaussian noise of zeromean. The filter used was a 5^{ t h }order Butterworth lowpass filter with a 3 dB cutoff frequency of 20 Hz. Electronic acquisition noise was simulated as a zeromean, additive, white Gaussian noise process.
2.2.2 Influence of the algorithm parameters
Ranges and values for the MLSS algorithm parameters
Parameter  Symbol  Min.  Max.  Optimal 

Median filter order  L  3  11  5 
Artifact detection threshold  U  8 ⋅ 10^{− 3}  5.23 ⋅ 10^{− 2}  2.23 ⋅ 10^{− 3} 
Polynomial order  Q  2  12  8 
Window semilength  M  7  18  13 
In order to analyze the effect of the parameters in the algorithm performance, Sobol sensitivity analysis was performed [25]. Using Sobol analysis, the total variance of the average P_{ i n } of 100 scanning signals was decomposed in terms which can be attributed to each of the algorithm parameters or to combinations of them [25]. All order indices, including the totaleffect indices, were calculated [1]. A total of 4000 samples of the parameter space were used to compute the indices. In this way, uniform random sampling of the parameter space was used, within the ranges of the algorithm parameters given in Table 1 (Min. and Max. values).
2.2.3 Influence of level of muscle contraction
 Error power outside the recording region where the physiological activity is located$$ P_{out} = 10\,\log_{10} \frac{{\sum}_{k = 1}^{K} {\sum}_{n = 1}^{N} (1z_{n,k})e_{n,k}^{2}}{{\sum}_{k = 1}^{K} {\sum}_{n = 1}^{N}(1z_{n,k})} $$(15)

The difference between the 3, 5, and 7point median algorithms and the MLSS algorithm in terms of the error power outside the physiological activity region, G_{ o u t }.

The difference between the 3, 5, and 7point median algorithms and the MLSS algorithm in terms of the error power within the physiological activity region, G_{ i n }.
2.2.4 Error distribution in the recording region
The aim of this experiment was to analyze whether the error associated with an algorithm is uniformly distributed throughout the recording or whether such an error tends to be concentrated in certain regions. To this end, for both median and MLSS algorithms, we studied the statistical behavior of the remaining error after the processing at each sample. Only one simulated MU was used, but the scanning recording procedure with that MU was simulated in 1000 independent runs. The percentage of MVC was 2.3% and was not varied. The noisy scanningEMG signal obtained in each run was processed by both algorithms and the error at the output of the algorithms e_{n,k} was calculated. To statistically characterize the error distribution in the recording region, we calculated the bias \(\hat {\mu }_{n,k}\) and the standard deviation (SD) \(\hat {\sigma }_{n,k}\) of the 1000 runs.
2.2.5 Application with real scanningEMG signals
The applicability of the algorithm was tested using real scanningEMG recordings. Note that, when dealing with real scanningEMG signals it is not possible to objectively quantify the algorithm performance, as the physiological noisefree version of the recorded scanningEMG signal is not available. This issue has already been discussed in other EMG studies [4]. It is possible, instead, to analyze the effects of the processing algorithms by comparing the waveform of the resultant scanningEMG signals. To this end, four real cases are presented in this paper, in which a real scanningEMG signal was processed by both the MLSS and the 7point median algorithms. The MLSS algorithm was used with the optimal parameters shown in Table 1.
The real scanningEMG signals used were selected from a set of 20 recordings performed in the biceps brachii of five normal subjects (3 male and 2 female) aged between 24 and 54 years. Informed consent was obtained from all subjects, and the study was approved by the ethics committee of Public University of Navarra. The scanningEMG recordings were obtained following the recording protocol described in [30], with sampling frequency of 20 kHz and scanning steps of 50 μ m. A concentric needle was used as scanning electrode and a facial concentric needle was used as trigger electrode. The scanning electrode was inserted 30 mm away from the trigger electrode along the longitudinal axis of the muscle.
3 Results
3.1 Influence of the algorithm parameters
3.2 Influence of level of muscle contraction
The results of G_{ o u t } and G_{ i n } at different levels of muscle contraction are depicted in Fig. 5c, d. The lower the order of the median algorithm, the higher the G_{ o u t }, which was positive in the vast majority of runs with the 3 or 5point median algorithm. The G_{ o u t } median was ranged between 3.4 and 5.68 dB for the 3point median algorithm, and between 0.27 and 1.74 dB for the 5point median algorithm. With the 7point median algorithm, G_{ o u t } was negative for all MVC values but low in magnitude, ranging between − 1.44 and − 0.39 dB. Regarding G_{ i n }, in the vast majority of the simulation runs, it was positive at all of the contraction levels investigated, and for any order of the median algorithm. The G_{ i n } median ranged between 2.55 and 4.11 dB with the 3point median algorithm, between 2.48 and 3.26 dB with the 5point median algorithm, and between 2.63 and 4.97 dB with the 7point median algorithm.
3.3 Error distribution in the recording region
Regarding error SD (Fig. 6d, e), outside the region of physiological activity, this SD was approximately constant for both algorithms (between about 0.8 and 1.3%). Within the physiologically active region, however, the SD with the median algorithm (which reached 3.6%) was greater than outside this region (Fig. 6d). In fact, the distribution of the error SD for the median algorithm was strongly correlated with the first difference of the scanningEMG signal in the spatial dimension (Fig. 6f), which means that regions of higher slope in the spatial dimension present a higher SD error. With regard the MLSS algorithm, on the other hand, the error SD within the physiological region barely increases respect to that of the nonphysiological recording region (Fig. 6e).
3.4 Application with real scanningEMG signals
4 Discussion
4.1 Algorithm performance
Potentials from nearby motor units are the principal source of contamination in scanningEMG recordings [20], and a signal processing technique that effectively removes such contamination with low distortion is therefore required [10, 11, 20] so that subsequent analysis of the scanningEMG signal is reliable and accurate. To this end, the current study presents and evaluates the MLSS algorithm compared to the median algorithm. Test results indicate that the algorithm removes artifacts from nearby motor units effectively and does so with low distortion of the scanning signal waveform, which is a major advantage over the median processing algorithm.
With regard to removal of artifact contamination, when dealing with the parts of a signal recorded outside the region of physiological activity, the error power of the MLSS is lower than that of the 3 or 5point median algorithm. The error power of the MLSS is higher only when compared to the 7point median algorithm, which we found to be the most effective of the median algorithms at contamination removal (Fig. 5a and c), these differences are however small (median G_{ i n } between − 1.44 and − 0.39 dB) (Fig. 5a, c).
Within the region of physiological activity, the error power of the MLSS algorithm is lower than that of the median algorithm for any order of the median filter in median algorithm (Fig. 5b, d); the median of G_{ i n } can be up to 4.9 dB when comparing to the 7point median algorithm (Fig. 5d). This suggests that the MLSS algorithm distorts the physiological waveform less than the median algorithm does. With regard to distortion, the MLSS algorithm performed better than the median algorithm over a wide set of scanning signals and at increasing amounts of artifact contamination resulting from higher levels of simulated muscle contraction (Fig. 5b, d).
It is well known that the distortion produced by the median filter tends to clip the peaks of a scanningEMG signal [10, 11, 20]. In the trials with real scanningEMG signals, peak clipping was observed for the median algorithm but not for the MLSS algorithm (Fig. 7). In the tests with simulated signals (Section 3.3), the error distribution of the median algorithm had negative bias in regions where there were scanningEMG signals peaks (Fig. 6a, c in n = 85, k = 35), which implies that peak clipping was systematically occurring in these zones throughout the multiple runs of the simulation experiment. In the case of the MLSS algorithm (Fig. 6b), the corresponding bias values were lower than those of the median algorithm (bias between − 12% and 5.95% of maximum amplitude for the median, and between − 4.83% and 3.9% for the MLSS), indicating that distortion was less severe (Fig. 6a).
Another kind of distortion in scanningEMG signals processed with the median algorithm was stepping in the amplitude profile of the scanning signal in the spatial dimension. To the best of our knowledge, this effect has not been described before in published studies; we observed the effect in both simulated (Fig. 8b) and real scanning signals (Fig. 7b, e, f, h). Stepping was associated with an increase in error SD in the recording area where physiological activity was located, especially in regions of the scanning signal with a pronounced slope in the spatial dimension (Fig. 6d, f). This is consistent with the fact that the 7point median algorithm presents a significantly higher error power within the physiologically active region than outside of it (Fig. 5a and b). With regard to the MLSS algorithm, the processed signals presented a smooth waveform (Fig. 7) which, in the case of simulated signals (Fig. 8c), was similar to that of the noisefree ideal scanningEMG signal (Fig. 8d, P_{ i n } = − 55.4 dBm). Accordingly, inside the physiologically active region, error SD with the MLSS algorithm was low, in fact, the difference between the error SD inside and outside the physiologically active region is small as can be observed in Fig. 6e.
4.2 Parameter settings
With regard to selecting a suitable set of parameters, the sensitivity study indicates that the algorithm performance is very influenced by the polynomial order Q (being its firstorder index 49% of the total variance), and also by the interaction between the window semilength M and Q (27.8%). The tradeoff between Q and M determines the ability of the polynomial to track variations of the scanningEMG signal in the spatial dimension. The higher the Q, or the lower the M, the greater the ability to track fast variations, which implies less waveform distortion when dealing with sharp scanning signals, but also less ability to remove artifact contamination. The median filter order, L has significant influence in the algorithm performance (firstorder index 12.3%), but the artifact detection threshold U it is not, at least in the range of parameters studied. These two parameters are related with the artifact detection effectiveness. A high L value involves a better artifact elimination, but it may also cause waveform distortion in sharply scanning signals, due to false artifact detections in the signal peaks.
Thus, the suitable parameter configuration will depend on the recording conditions of the scanningEMG signal. For instance, when dealing with scanning signals presenting sharp peaks in the spatial dimension, parameter settings that imply low distortion should be selected. On the other hand, if the recorded signal has a very high level of artifact contamination, it may be desirable to select a parameter configuration that prioritizes the noise elimination instead. Despite that, the optimal algorithm parameters obtained in our study (see Table 1) can in the first instance be a good configuration to be routinely used, as using these parameters, the algorithm was able to work properly in scenarios with different levels of artifact contamination (different levels of voluntary contraction) and with a large set of scanningEMG signals.
5 Conclusion
An algorithm based on masked leastsquares smoothing has been proposed for and evaluated in the processing of scanningEMG signals. Simulation experiments show that the new algorithm overcomes limitations of the median algorithm: stepping in the amplitude profile and peak clipping. Furthermore, the tests indicate that, over the studied range of muscle contraction levels, the new algorithm performed with noticeably less distortion of the signal waveform than the median algorithm, while effectively removing noise and artifacts from nearby MUs.
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