1. Introduction
The magnitude of the muscle force or joint torque generated during neuromuscular electrical stimulation-evoked contractions has been used as a marker of physical performance in healthy individuals [
1,
2], as well as a benchmark of functional recovery in individuals with neurological conditions [
3,
4]. To optimize neuromuscular electrical stimulation (NMES) technology in therapeutic and functional applications, real-time information about the generated muscle force or joint torque, of the controlled limb, is vital [
3,
5]. Such information is required; (i) to automate the neuromuscular stimulation characteristics based on the muscle state during the onset of fatigue; and (ii) to modulate muscle forces based on the requirements of the task (therapeutic or functional) to be performed, for example during sit-to-stand and sustained standing perturbations. However, joint torque is often impractical or impossible to quantify directly during real-time application of NMES [
5]. Estimation of joint torque from readily available muscle characteristics (e.g., biopotentials of nerve and/or muscle activation), particularly, from physical sensors has recently become both viable and attractive [
5].
One such neuromuscular biopotential is the Mechanomyographic signal (MMG), which quantifies the mechanical equivalent of an electromyographic output generated during muscle contractions [
6,
7]. The signal originates from the skeletal muscle contractions due principally to the shortening of the muscle fiber length and increase in its diameter [
7,
8]. The activation of muscle fibres and their dimensional changes during muscle contraction creates pressure waves that can be detected on the skin surface and translated into an acceleration obtained by physical sensors, such as an accelerometer [
9]. The signal can represent a proxy for neuromuscular contractions [
10] and has gained recent popularity due to its close relationship with muscle force [
11]. Specifically, the signal is directly related to the two main force-generating mechanisms of human skeletal muscle—magnitude and pattern of motor unit recruitment and their firing rates/frequency [
12,
13].
Moreover, due to the convenience of MMG signal collection, its insusceptibility to skin impedance [
14], flexibility of its sensing technology [
15,
16], and immunity from electrical stimulation artifacts associated with NMES [
17], the signal has been successfully used to classify muscle activity for specific application in controlling prostheses [
18], and as a control signal for muscle machine interfaces [
16,
19]. In addition, during NMES-evoked muscle contractions, MMG has been used to track muscle fatigue in healthy volunteers [
20]. Thus, the signal may be used to estimate joint torque during voluntary and/or NMES-evoked muscle contractions [
7]. However, relating MMG signals as a direct proxy for NMES-evoked muscle effort/force can be practically challenging due to the complexity and diversity of the recruitment of muscle’s motor units (MUs) [
6,
18]. Accordingly, the application of computational intelligence techniques for quantification of joint torque from MMG signals has been proposed through statistical predictive modelling, and then validated during voluntary contractions [
13,
21].
The use of machine-learning techniques has recently shown promise, subverting the dual problems of non-linearity and non-stationarity in estimation, prediction and classification tasks. For example, Youn and Kim [
13,
22] used an artificial neural network model to estimate elbow flexion force from MMG during voluntary isometric contractions. The investigators obtained an estimation accuracy of up to 0.892 [
13] and 0.883 [
22] in terms of cross-correlation coefficient, and concluded that their model is subject dependent, while suggesting the future application of other machine learning techniques including Support Vector Regression (SVR) to improve the estimation accuracy of the model [
22]. However, due to the advancement in the field of signal processing, several other computational intelligence statistical regression techniques have been proposed with SVR yielding a good predictive and estimation accuracy, with often low Root Mean Square Errors (RMSE) [
23] and outstanding performance [
21]. Being a category of support vector machine learning technique, SVR is based on the principles of computational intelligence that is built on the kernel method (that maps data into higher dimensional space where the training sample may be linearly separable to facilitate linear regression analysis) [
24]. SVR algorithms take into account the error approximation to a dataset with the ability to adapt and improve the estimation capability of a model [
23], particularly when the model is used to evaluate an additional dataset for the purpose of generalization [
25,
26]. Moreover, SVR is robust in handling multivariate processes and offsets the limitation of traditional regression methods [
27]—which cannot solve problems with high dimensional input dataset [
24]. Additionally, the SVR modelling only involves a solution to a “convex optimization problems”, and unlike ANN model, it is not influenced by the “local minimal problem” [
28]. Thus, the SVR algorithms could be used to build a generalized model and well suited for regression tasks [
24]. Based on this strength, the technique has been successfully deployed in several fields of applications including physical therapy and exercise science during voluntary muscle activation [
21], medical diagnosis [
29], and a host of other related fields. However, to our knowledge, SVR modelling has not been previously used to construct a joint torque estimation model, particularly, during electrically stimulated contraction.
The purpose of this study was, therefore, to use SVR modelling to predict knee extensor joint torques from MMG signal characteristics during NMES-evoked incremental muscle contraction intensities. Since it has been suggested [
13] that a combination of muscle contraction signals and related characteristics could compliment the estimation accuracy of joint torques, three input parameters (related to muscle contractions) to the SVR model were chosen (MMG signals, level of electrical stimulation or contraction intensity, and knee angle) to estimate knee torque accurately. This information is particularly applicable to research areas where a real-time proxy of muscle force is sought.
3. Results and Discussion
Table 2 describes the actual experimental dataset used in this study. The results of the statistical analysis of the dataset are presented in
Table 3. The suitability and applicability of the chosen dataset are revealed from the mean, maximum value, median, standard deviation, and minimum value. The MMG-RMS, MMG-PTP, level of electrical stimulation or contraction intensity, and knee angle obtained experimentally were the input to the SVR model to estimate the knee torque. Results of performance measures obtained from the training subset and testing subset are as shown in
Table 4.
To our knowledge, this is the first attempt to use a SVR modelling technique for NMES-evoked knee torque estimation from MMG signal. The outcomes of the developed SVR model (
Table 4) indicated high correlation as well as low RMSE, and the model could, therefore, be adjudged as accurate. Moreover, high accuracy of the trained system as evident by the coefficient of determination (
R2 = 94%), in predicting knee torque confirmed a reliable pattern between the predictors and the outcome which might be otherwise difficult to learn using linear regression.
During the training period of the model, the estimated torques were positively correlated with the actual values drawn from the experimental data (actual vs. predicted values) for both the training (
Figure 4A) and testing (
Figure 4B) subsets.
In addition, the cross-plots of the “training’’ subsets (actual vs. predicted values) as shown in
Figure 5 also confirmed the high accuracy of the “training” subsets. However, since the actual performance of any model is better accessed by the testing outcome [
55], the accuracy of the developed SVR model was tested using 30% of the available data samples (i.e., the reserved 30% that was not used in model development). It was interesting to note that, the model also performed satisfactorily during testing phase (
R2 = 89%).
This high correlation indicated that the estimated knee torque by the SVR model was very close to the actual experimentally recorded joint torque (from an isokinetic dynamometer) for each data sample. For better visualization and understanding of the outcome of this study, the cross-plot of testing sets (actual vs. predicted values) has been portrayed in
Figure 6. The level of accuracy in the testing phase (
R2 = 94%) of the model development indicates that the model is stable, efficient and not over-fitted. This was based on the suggestion of Tay and Cao [
56] that an overfitted model could perform excellently on the training set (
r > 0.90) but will perform poorly on testing set [
56]. Therefore, the developed SVR model in this study achieved a good performance for both training and testing sets. These results are comparable to that of Youn and Kim [
22], where an artificial neural network model has been successfully used to estimate elbow force during voluntary contractions. Meanwhile, the potential of the SVR model for NMES-evoked joint torque estimation which has not been previously documented has also been demonstrated in our study.
Moreover,
Figure 5 and
Figure 6 portrayed the closeness of the predicted torque by the proposed SVR model to the actual experimental values. It could be noted that almost all the predicted points fit exactly on the experimental point or at least fits very closely to the target experimental point. Taken together, it could be inferred that the real-time knee torque information which is vital for the closed-loop implementation of NMES [
3,
5] in physical therapy and exercise science might be reliably estimated by our proposed method. Nevertheless, we acknowledge the following limitation in our study design: The performance of the developed model is limited to torque estimation during NMES-evoked isometric knee extension in healthy volunteers. In the future studies, we will verify the performance of the model using MMG signal and torque data from participants with neurological conditions. This will allow us to examine and improve the performance of the model, and to derive clinically relevant characteristics about the muscle force recruitment in clinical populations.
4. Conclusions
Based on its previous estimation accuracy in relevant fields, SVR modelling was used in this study through the integration of relevant variables to predict NMES-evoked knee torque. The model was developed through training and testing via test-set cross-validation technique with available dataset partitioned into training and testing subsets. Using the SVR methodology, the predicted knee torque was positively correlated with the actual values drawn from the experimental data for the training subset. Thereafter, to check the predictive ability of the model, the trained model was tested using the reserved testing subset that was not used in model development. The model performance was measured based on the correlation coefficient and RMSE. The outcomes from the developed SVR model showed an accurate prediction of the knee torque, characterized by high correlation coefficient—up to 0.97 and 0.94; and coefficient of determination—up to 94% and 89%, and low RMSE of 9.48 and 12.95, for the training and testing cases, respectively. These results, which have not been previously reported, indicated a close similarity between the estimated joint torque by the SVR model and the actual experimental data obtained from the laboratory experiment. Additionally, the present study has uniquely shown that a SVR model could estimate NMES-evoked knee torque, generated by a synchronous modulation of muscle fibres’ motor units [
57], from MMG signal. Therefore, the good performance achieved in this study will motivate further studies in a similar direction to facilitate accurate estimations of joint torque using datasets from clinical populations—in which the NMES technology is more relevant, particularly among those with spinal cord injury. Moreover, since SVR models can be adapted for classification tasks [
43], in the future, the developed model will be used to classify fresh and fatiguing muscle contractions of knee extensors, from MMG signals, during standing and ambulation tasks. Such models might offset the need to contend with the stimulation artifact [
3,
5] often encountered with the application of surface electromyographic signal as NMES feedback source.