Introduction

Electromyography is a technique for evaluating and assessing of electrical signals generated from a muscular movement. This accumulated electrical signal is known as an electromyogram (EMG) [1]. EMG is a useful tool for clinicians and researchers for the faithful diagnosis of neuromuscular disorders. These disorders are related to impacts on muscle, motor neurons, nerves and muscle tissues. EMG signals are important in enormous fields, like medical science, rehabilitation, ergonomics, and sports science. The vast usage of EMG is in medical research for identification and analysis of neuromuscular disorders, motor neurons by using an electrical activity of a signal [2, 3]. Electrical impulses produced by brain controls the function of muscles. The generated electrical impulses are carried to every fiber of muscles by motor neurons, familiar as a nerve cell. All disorders, which affects the working function of motor neurons creates various diseases [4]. The EMG signal is a valuable source for functioning and to show status of a muscle diagnosis of amyotrophic lateral sclerosis (ALS) and myopathy (MYO).

Motor neuron disorder creates a lot of diseases, mainly the ALS. ALS greatly impacts neuron groups which results in inability to control the voluntary movement of muscles in the body and also makes muscles more weaker and much smaller. ALS progressively damages nervous control because of which weakness, paralysis, respiratory failure and harm to cells in spinal cord and brain occur [5]. Myopathy is a non-progressive type neuromuscular disorder affecting people mostly between the age group of 20–50 years. Myopathy is a muscle disease, affecting mainly skeletal fiber muscles and is caused by inflammatory, metabolic and endocrine disorders. Myopathy effects bones of quadriceps and biceps muscles that results in muscles cramp, spasm, stiffness, and dysfunction. It stops proper working of muscles which means, it does not cause muscles to die and it makes weaker, but it affects mostly at the center part of a muscle. These diseases mimic with other diseases, so that early stage detection reduce pain in patient and medical expenses [4, 6]. The visual inspection of neuromuscular disorders by using EMG is a laborious task due to nonstationary nature of a signal. For that reason, the diagnosis of neuromuscular disorder of EMG signals requires an accurate and automatic methodology.

Extracted parameter from EMG signals is useful for analysis of diagnostics. The parameters extraction mainly depends on time, frequency, and time-frequency domain. The time-frequency based short time fourier transform (STFT), frequency based mean frequency, and time based ZCR, ACR features are used with KNN in order to classify the myopathy and normal EMG signals [6]. The time based features are autocorrelation (ACR), zero crossing rate (ZCR), and spectral features are mean frequency, spectral peak which classify myopathy and normal EMG signals [7]. Features extracted from analytic IMF are area computation, mean of first derivative instantaneous frequency are used for discrimination of myopathy and normal EMG signals by using kruskal-wallis test [8]. The frequency cepstrum based mel-frequency cepstral coefficient (MFCC) features input to K-nearest neighborhood (KNN) classifier for classification of ALS and normal EMG signals [9]. Extracted analytical features are area computation, normalized instantaneous frequency \((IF_{n}),\) a spectral moment of PSD \((SM_{PSD}),\) and the first derivative of instantaneous frequency \((\textit{MFD}_{IF})\) features with LS-SVM classifier are used to classify ALS and normal EMG signals [5]. The image extracted features that are time-frequency based spectrogram, Wigner–Ville distribution, STFT, and continuous wavelet transform (CWT), are employed to give a conventional neural network for classification of ALS and normal EMG signals [10, 11]. An improved EMD (IEMD) algorithm and Hilbert transform are extracted and its bandwidth features \(B_{AM},\) \(B_{FM},\) \(SM_{PSD},\) and \(\textit{MFD}_{IF}\) are used to discriminate between the ALS and the normal EMG signals [12]. Extraction of MUAP features with higher energy DCT coefficients are used as features with KNN classifier to classify the ALS and normal EMG signals [13].

From EMG signals to extract time based MUAPs features and entropy-based features like spectral, sample, approximate, fuzzy entropy from TQWT sub-bands. These features will be used for the classification of MYO-NOR EMG signal and ALS-NOR EMG signal by using random forest classifier [14]. The ELM classifier classifies EMG signals based on extracted bispectrum based features, fractal dimension features [15]. The extracted temporal feature, DWT based spectral feature, and direct extraction of spectral features are peak frequency, mean frequency, total power, and median frequency are given to KNN classifier for classification of ALS, myopathic, and normal EMG signal [16]. Multi scale principal component analysis (MSPCA) denoising method presented to decomposition method of multiple single classification (MUSIC) for extraction of features. The KNN, ANN, and SVM are used for classifying ALS, myopathy, and normal EMG signals [17]. The MUAP selection by windowing of EMG signal is based on the highest energy of a divided signal. The statistical DWT features extracted from MUAP are maximum energy of a wavelet. These classify neuromuscular diseases using KNN and LSSVM classifiers [18]. Feature extraction of DWT based decomposition method with MSPCA denoising approach classifies ALS, myopathy, and normal EMG signals by using decision tree algorithms [19].

In this paper, adaptive signal decomposition method VMD is used for decomposition of EMG signal into modes. spectral and statistical features namely spectral flatness (SF), spectral spread (SS), spectral decrease (SDec), kurtosis, MAD, and IQR are used for classification of the neuromuscular disorders. The remaining paper has been depicted as follows: the EMG dataset, the variational mode decomposition method is presented in “Methodology”. The extracted features from modes and ELM classifier are present in the upcoming “Feature extraction”. The results and discussions from simulations are used for classification of ALS, myopathy, and normal EMG signal as explained in “Results and discussions”.

Methodology

The block diagram of proposed method is shown in Fig. 1.

Dataset

The online link http://www.emglab.net [20] gives us the dataset of the recorded EMG signals. Dataset has three main groups such as ALS, myopathy, and normal. ALS group consists of eight subjects: 4 male and 4 female age group of 35–67 years. Five subjects from ALS group died within few years after the occurrence of disease. Myopathy group consists of seven subjects: 2 male and 5 female age group of 19–63 years. In normal group, ten subjects as 6 males and 4 females of age 21–37 years are present. No one from the normal group has any signs or history of neuromuscular disorders. Brachial biceps muscles are used for investigating these three groups. Signal acquisition is achieved using a standard needle electrode having area of 0.07 mm2. Tuning sampling rate was 24 KHz and digitized by A/D converter contained the resolution of 16 bits. Recorded signal was filtered by a high and low pass filters set to 2 Hz and 10 KHz respectively, (i) The signal quality is monitored by using visual and audio feedback, (ii) EMG amplifier uses the set of 2 Hz and 10 KHz low and high pass filters, (iii) Signal collection is through three level insertion from five various places, (iv) Recording was made at above threshold and constant level of contraction. In this 89 ALS, 107 myopathy, and 133 normal EMG signals [20] are being used with following considerations.

  • Case 1 One abnormal class forms the ALS class and subset of healthy class forms the normal (NOR) class.

  • Case 2 One abnormal class forms the myopathy (MYO) class and subset of healthy class forms the normal (NOR) class.

  • Case 3 Subset of ALS, MYO forms the abnormal class and subset of healthy class forms the NOR class.

Fig. 1
figure 1

Overview diagram of EMG signals classification using VMD method

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Variational mode decomposition

Variational mode decomposition (VMD) decomposes a real-valued signal into a band-limited variational mode function or modes (\(u_k\)). These modes occur concurrently and exhibit specific sparsity property to reproduce an input signal [21]. So, VMD nonrecursively decomposes signal into k modes (\(u_k\)), each compact around its own center pulsation \(\omega\). Before formulation of the constrained optimization problem, we compute the analytic signal to get a unilateral frequency spectrum using Hilbert transform. The frequency shifting property is applied on each mode tuned to the corresponding center frequency. Its bandwidth is predicted by applying H1 Gaussian smoothness to the demodulated signal. The constrained variational problem is expressed as [21]

$$\begin{aligned} &{\min _{\{ {u_k}\} ,\{ {\omega _k}\}}}\left\{ {\sum \limits _k {\left\| {{\partial _t}\left[ {\left( {\delta (t) + \frac{j}{{\pi t}}} \right) * {u_k}(t)} \right] {e^{ - j{\omega _k}t}}} \right\| _2^2}} \right\} \\ &\text{{subject\;to}}\;\;\sum \limits _k {{u_k}} (t) = x(t) \end{aligned}$$
(1)

The Lagrangian multiplier \({(\lambda )}\) and a quadratic penalty factor \({(\alpha )}\) converts (1) into unconstrained optimization problem as addressed below (2)

$$l({u_{k}},{\omega _k},\lambda ) :=\alpha {\sum _{k}\left\| \partial _t \left[ \left( \delta (t)+\frac{j}{\pi t}\right) \ast u_k(t)\right] {e^{^-j \omega _k t}}\right\| ^{2}_{2} + \left\| x(t)-\sum _{k} u_k(t)\right\| ^{2}_{2}+\left\langle \lambda (t), x(t)-\sum _{k} u_k(t)\right\rangle }$$
(2)

Above augmented lagrangian function \((\ell )\) is used to solve (2) by using the alternate direction method of a multiplier (ADMM). ADMM is an optimization technique to estimate center frequencies and modes centered around their frequencies in the spectral domain. The embedded wiener filter in VMD updates optimally each mode \(u_k(\omega )\) and center frequency in the fourier domain. The VMD algorithm for decomposition of EMG signal shown below.

figure a

The decomposed modes of ALS, myopathy and normal EMG signals are shown in Fig. 2a, b, and c, respectively, which signifies that the higher modes shoes higher frequency oscillations.

Fig. 2
figure 2

Example four modes of VMD a ALS signal, b myopathy signal, c normal EMG signal

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Feature extraction

Spectral features

If x(n) is an N sample EMG signal and X(m) gives the magnitude spectrum of x(n).

  1. 1.

    Spectral flatness (SF) Noisiness of the magnitude spectrum gives the SF. The signal spectrums geometric mean to arithmetic mean ratio determines SF. It can be denoted [22, 23] as:

    $$\textit{SF}= {\frac{\prod _{m=0}^{N-1}{|X(m)|^\frac{1}{N}}}{\frac{1}{N}\sum _{m=0}^{N-1}|X(m)|}}$$
    (8)
  2. 2.

    Spectral spread (SS) Sometimes known as instantaneous bandwidth, given by magnitude spectrum concentration around spectral centroid. Standard deviation of magnitude spectrum around spectral centroid can also be assumed as SS. Mathematically, SS can be described [22, 23] as:

    $$\textit{SS}= {\frac{\sum _{m=0}^{N-1}{(m-\textit{SC})^2 {|X(m)|}}}{\sum _{m=0}^{N-1}|X(m)|}}$$
    (9)

    Frequency weighted sum of magnitude spectrum of signal normalized by its unweighted sum is SC i.e. center point of spectrum can be given as

    $$SC={\frac{\sum _{m=0}^{N-1}{m {|X(m)|}}}{\sum _{m=0}^{N-1}|X(m)|}}$$
    (10)
  3. 3.

    Spectral decrease The slope at which the spectral envelope decreases with respect to frequency gives the spectral decrease (SDec) [22]. SDec is denoted [23] as

    $$SDec={\frac{\sum _{m=1}^{N-1}{\frac{1}{N} {(|X(m)|-|X(0)|)}}}{\sum _{m=1}^{N-1}|X(m)|}}$$
    (11)

Statistical features

  1. 1.

    Kurtosis In this work, we used statistical moments such as kurtosis which shows the peaked nature of time series [24]. Mathematically it can be expressed as

    $$k={\frac{1}{N}\sum _{m=1}^{N}{\left( \frac{x_m-\mu }{\sigma }\right) ^{4}}}$$
    (7)
  2. 2.

    Mean absolute deviation It is difference between actual value and their mean value of variational modes [25]. It is formulated as

    $$MAD={\frac{1}{N}\sum _{m=1}^{N}|x_m-\mu |}$$
    (8)
  3. 3.

    Inter quartile range It gives a variability of measuring data set. It is defined by difference of 75th and 25th percentiles samples of modes [24] as given by

    $$IQR={Q_3-Q_1}$$
    (9)

    Here, \(Q_1\) and \(Q_3\) are first and third quartile respectively.

Total six-features are extracted for each class EMG signals. The dimensions of feature vectors for ALS, myopathy, and normal classes are \(89\times 6,\) \(107\times 6,\) and \(133\times 6,\) respectively. Feature normalization is needed when there is a large variation in different classes or size of the feature is large. At that time, it shows biased classifier nature towards a particular set of attributes. The unit length feature normalization method is applied on extracted features [26].

Extreme learning machine (ELM)

A feed forward neural network with single hidden neuron is termed as ELM in which first weighted matrix is selected arbitrarily. It enables the fast estimation of output matrix using the least square method [27]. ELM due to its simple structure and high training speed is advantageous for multi-class classification of N number of arbitrary samples (\(x_r, t_r\)). Here \({x_{r} = [x_{r1},x_{r2},\ldots , x_{rn}]^T}\) and \({t_{r} = [t_{r1}, t_{r2},\ldots , t_{rn}]^T }\). The simplified architecture of ELM classifiers is shown in Fig. 3.

A single hidden layer feed forward neural network having the activation function g(x) and a number of hidden layers can be given by:

$${\sum _{r=1}^{N} \beta _{r} g_{r}(x_r)= \sum _{r=1}^{N} \beta _{r} g(a_{r}. x_{i}+b_{r})=t_{i}}$$
(10)

By using the weight vector of \({a_{r}=[a_{r1},a_{r2},\ldots ,a_{rn}]^T}\) for connected to rth hidden input node and output node is connected to rth hidden node by the weight vector \({\beta _{r}=[\beta _{r1},\beta _{r2},\ldots ,\beta _{rn}]^T}\). where \(b_{r}\) is the threshold of rth hidden node, above objective function and inner product as shown in [28].

Fig. 3
figure 3

The structure of the ELM classifier with input training samples

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Results and discussions

VMD method is used to decompose EMG signals into various modes from which spectral and statistical analysis features namely SF, SS, SDec, Kurtosis, MAD, and IQR are extracted and have been used for the classification of neuromuscular disorder of EMG signals. Tables 1 and 2 show clearly the spectral and statistical features range of mean and standard deviation of ALS, myopathy, and normal EMG signals. In Table 1, SS and SDec features show a higher value for myopathy signals compared to other EMG signals for all modes except the first mode. Myopathy signals have higher SS because of the change in spreadness of spectrum and higher spectral decrease. In myopathy signal, the higher SDec is because of the variation in spectral envelope of the signal. In Table 1, spectral flatness shows a higher value for normal EMG compared to other EMG signals for all modes except the second mode. Higher SF in normal EMG signal is due to the presence of lower noisiness in the signal. In Table 2, IQR is higher in ALS signals compared to other signals except for the third and fourth mode. The higher value signifies the variability of the signal. In Table 2, kurtosis exhibits a higher value for myopathy signals compared to other EMG signals, because of its high peaked nature. In Table 2, MAD feature of ALS signals is higher for all modes due to their higher amplitude variation compared to other EMG signals.

The modes of ALS signal, myopathy signal, and normal EMG signal obtained using the VMD method represent band-limited frequency components. The ELM is a popular classifier and is used in various biomedical signal classifications. In m-fold cross-validation, the data is broken into m parts. Each \(m-1\) subsets at a time are used for training the classifier, and the remaining each one subset is used to test the classification model. ELM classifier provides satisfactory classification performance of signal with 10-fold cross-validation procedure. Simple structure and multiclass classification without any change in classifier parameters is provided by ELM classifier. It is extremely useful for the multi class EMG signals classification. Classification performance of ELM classifier is in terms of sensitivity (SEN), specificity (SPE), and accuracy (ACC) [29]. These can be expressed as:

$$\textit{SEN}=\frac{\textit{TP}}{\textit{TP}+\textit{FN}}$$
(11)
$$\textit{SPE}=\frac{\textit{TN}}{\textit{TN}+\textit{FP}}$$
(12)
$$\textit{ACC}=\frac{\textit{TN}+\textit{TP}}{\textit{TN}+\textit{TP}+\textit{FN}+\textit{FP}}$$
(13)

TP and FP signify true positive and false positive rate of normal class EMG signals. TN and FN signify true negative and false negative rate of abnormal class EMG signals. In Tables 3, 4 and 5, mode wise classification performance of the ELM classifier is in terms of SEN, SPE, and ACC of ALS-NOR, MYO-NOR, and ALS-MYO-NOR EMG signals. The overall classification performance of Cases 1–3 EMG signals based on accuracy is 98.52%, 99.50%, and 97.75% and are highest for the first mode among all modes.

The confusion matrix of the respective EMG signals of the first modes is shown in Tables 6, 7 and 8. The detection rate of normal EMG is higher compared to ALS signals as shown in Table 6. It gives better classification rate for ALS-NOR signals with an accuracy of 98.52% for the first mode. Table 7 shows less misclassified myopathy and normal EMG signals. The detection rate of MYO-NOR gives an accuracy of 99.50% by ELM for the first mode. Table 8 shows a detection rate of myopathy and normal EMG signals compared to ALS signals is higher, but overall classification accuracy of ALS-MYO-NOR are 97.75% for the first mode by ELM classifier.

Table 1 Range (mean ± SD) values of the SF, SS, SDec features for the MODES
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Table 2 Range (mean ± SD) values of the Kurtosis, MAD, and IQR features for the MODES
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Table 3 SEN, SPE, and ACC of modes with ELM classifier for classification between ALS and normal EMG signals
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Table 4 SEN, SPE, and ACC of modes with ELM classifier for classification between MYO and normal EMG signals
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Table 5 SEN, SPE, and ACC Modes with ELM classifier for classification between ALS, MYO, and normal EMG signals
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Table 6 Confusion matrix of ALS and normal EMG signals for Mode 1 by ELM classifier
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Table 7 Confusion matrix of myopathy and normal EMG signals of Mode 1 by ELM classifier
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Table 8 Confusion matrix of ALS, MYO, and normal EMG signals for Mode 1 by ELM classifier
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Table 9 Comparison of classification between ALS and normal EMG signal performance with same dataset
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Table 10 Comparison of classification between and myopathy signal and normal EMG signal performance with same dataset
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Table 11 Comparison of classification between ALS-MYO-NOR EMG signals performance with same dataset
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In Tables 9, 10 and 11 present a comparison with the proposed method and other existing methods in the literature for ALS-NOR, MYO-NOR, and ALS-MYO-NOR detection which has been studied on the same EMG dataset. It is clear from the Tables 9, 10 and 11 that the proposed method has provided better classification performance as compared to existing methods. It has been observed VMD decomposes signals into variational modes having the robustness to noise and sampling. The extracted spectral and statistical features given a good response to classification of EMG signals. These results show that proposed methodology provides better performance for automatic identification of neuromuscular disorder.

Conclusion

In this paper, the identification of neuromuscular disorder of ALS, myopathy is carried out using VMD-based features. VMD concurrently decomposes EMG signals into modes, which are used in extraction of features like SF, SS, SDec, kurtosis, MAD, and IQR. The extracted features are normalized using unit length normalization method and fed as inputs for the ELM classifier in order to classify neuromuscular disorders. A classification accuracy of 98.52%, 99.50%, and 97.75% corresponds to ALS-NOR, MYO-NOR, and ALS-MYO-NOR classes is achieved for the features extracted with the ELM classifier for the first mode. SEN, SPE, and ACC parameters are showing good results. The classification results of proposed method shows a better performance in comparison to other existing methods. The suggested method can be beneficial for the diagnosis of neuromuscular disease in clinical application.