Amputees regain functional abilities by learning to use a prosthesis (Windrich et al., 2016). Most prostheses are passive and are adequate for most walking scenarios in daily life. However, these passive prostheses are not capable of producing power. Therefore, the use of these prostheses in daily life is limited by an amputee’s strength and capacity for gait adaptations. This makes activities such as stair climbing challenging (Dabiri et al., 2010; Crowe et al., 2019). Actuated or powered prostheses have the potential to overcome these limitations by providing net power (Windrich et al., 2016). Commercially available powered prostheses use state-machines to provide control in predefined states. The downside of this approach is that the control is limited in intuitiveness and the user is not able to use the prosthesis outside of predefined states. Direct control over the knee joint might result in a more intuitive control of the prosthesis, which can be beneficial for the user during various tasks of daily living. It can be beneficial to apply direct control within a discrete state, for example to reposition the prosthesis while sitting or to control the speed of a motion. Surface electromyography (EMG) can play a large role in creating intuitive control, as EMG can be measured 138 ms before the onset of movement (Wentink et al., 2014). Other sensor information related to movement, such as acceleration, will always lag behind the intended motion and will result in a delay within the control scheme. EMG does not suffer from this delay and translating EMG into joint torque is therefore a promising method to realize voluntary control.

Machine learning can be a viable tool for joint torque prediction. Neural networks are a type of machine learning algorithms that are trained to find the underlying relation between input and output variables. Several studies used neural networks for the prediction of knee flexion angles or torques in able-bodied subjects (Liu et al., 2018; Huang et al., 2019; Saranya et al., 2019; Wang G. et al., 2019; Deng et al., 2020; Gautam et al., 2020). Huang et al. (2019) proposed a deep-recurrent neural network for prediction of knee joint angles in real-time. The model used EMG signals together with inertial data from different activities and reported a root mean squared error of 2.93° over a range of approximately 60° (4.9% error). Gautam et al. (2020) used a Long-term Recurrent Convolution Network to classify movements and predict their corresponding knee joint angles, based on EMG. They reported an average mean absolute error of 8.1% in the knee angle prediction of healthy subjects. Zhang et al. (2020) developed an artificial neural network for the prediction of ankle torque from EMG. Root mean squared error (RMSE) values ranging within 0.01 and 0.10 Nm/kg were found for ankle plantar- and dorsiflexion on a range of approximately 1.5 Nm/kg (0.7–6.7% error). All these studies show low error rates, which indicates that machine learning can be a valuable tool in predicting knee torque or knee angle. However, current machine learning decoders might produce unrealistic estimates in conditions they are not trained in as the algorithm are not limited by physical bounds (Sartori et al., 2018). Next to this, the reliability of these methods depend on correct electrode placement and are thus sensitive to changes in conditions. Futhermore, the amount of training data is also usually limited relative to the complexity of the models, which makes it difficult to obtain a satisfactory generalization performance (Wang W. et al., 2019). The robustness to EMG electrode placement, differences in EMG signals (quality), activity performance and performance over days is thus questionable and needs futher investigation.

One potential way to improve robustness, is the use of an NMS model. Neuromusculoskeletal (NMS) modelling was designed to gain insight in the underlying process of biomechanical movement to characterize motor function and how it alters with pathology (Durandau et al., 2019). An NMS model consists of multiple components that model this underlying process. It uses EMG and muscle characteristics from a musculoskeletal model to predict specific muscle activations with corresponding forces and resulting joint torques. An NMS model can provide system robustness since any joint moment estimate must always exist within the musculoskeletal model operational space and be therefore physiologically plausible (Sartori et al., 2018). Another benefit of using an NMS model is that it provides insight in the underlying process of biomechanical movement, whereas machine learning does not. Several studies used an NMS model to predict joint torque (Wang W. et al., 2019; Sartori et al., 2018; Durandau et al., 2019, 2018; Sartori et al., 2012, 2016; Kapelner et al., 2020). Sartori et al. (2012) developed a control scheme to control a wrist-hand prosthesis by real-time neuromusculoskeletal modelling. Joint torque was predicted using EMG and prosthesis angles as input and translated into low-level control of the prosthesis. They executed a virtual reaching test in which subjects reached targets using linear trajectories, thereby successfully actuating a single DOF at a time with high precision. Path similarity was always accomplished with R ² > 0.98 across all targets and subjects. Durandau et al. (2019) predicted lower limb exoskeleton support torque, using EMG and joint angles as input to an NMS model. The RMSE for the knee joint control, inside exoskeleton conditions, were 4.06 ± 2.55° for low gain and 4.58 ± 2.61° for high gain over a range of approximately 40° (approximately 10–11% error). Correlation coefficients of both conditions between prediction and reference torque were 0.90 ± 0.16 and 0.92 ± 0.07 respectively. Zhang et al. (2020) used an NMS model to predict ankle joint torque with RMSEs ranging from 0.04 to 0.18 Nm/kg for ankle plantar- and dorsiflexion on a range of approximately 1.5 Nm/kg (2–12% error). Downsides of NMS modelling workflow are that it can be complex and difficult to work with. Furthermore, the mapping of EMG to muscle activation is based on models that are difficult to validate because activations cannot be measured directly.

Since both machine learning and NMS models show several shortcomings, the question arises if combining these two methods into a hybrid version will provide better joint torque predictions. Machine learning can decrease computational demands in physics-based modelling. It can be used for feature extraction from measures of muscle activation and to synthesize missing data (Saxby et al., 2020). Cimolato et al. (2020) developed a machine learning driven NMS model to predict lower limb joint torque from EMG and inertial data to control a lower limb prosthesis during regular gait. They used a Gaussian Mixture Regressor to generate a complete set of EMG signals, starting from the supposed residual subset of available EMGs. These EMG signals were then used as input for a calibrated NMS model to predict joint torque, which resulted in an average normalized root mean squared error (NRMSE) of 24.0 ± 11.0%. Xu et al. (2020) developed an EMG-based elbow joint torque estimation strategy using a Hill-Type Muscle Model and a neural network. The neural network was used to estimate muscle activation which was used as input for the Hill-Type model. System identification from EMG signals was used to estimate the elbow angle. The average RMSE over trials was 1.45 Nm on a range of 25 Nm (5.8% error). Only one subject was used and three trials were conducted on the same day. Although these studies show lower accuracies than machine learning or neuromuscular modelling, the idea of combining neuromuscular modelling with machine learning still holds promise.

In the described studies we have seen that machine learning, neuromuscular modelling or a combination of both are promising approaches for knee joint torque estimation. Despite these positive results, to our knowledge, no commercial product is available that uses machine learning, NMS or a hybrid approach for direct control of a prosthetic knee. One of the reasons is that prostheses need to be used in daily life and need to function everyday in a reliable manner, being robust to different environmental conditions, such as electrode placement and skin conditions, but little is known of the behavior of these approaches over multiple days.

The goal of this study was to compare three model types to predict knee joint torque from EMG, to be used for multi-day control of a transfemoral prosthesis in non-weight bearing situations. In this work we used a convolutional neural network (CNN) using recurrent layers to predict knee joint torque, as this architecture is useful for biomedical time series modeling (Gautam et al., 2020). To our knowledge, CNNs have not been applied before for knee joint torque prediction. We evaluated the models over multiple days, to see their robustness when applied in a multi-day setting. Our expectations are threefold. Firstly, CNN models will show excellent performance on the training day, but performance will decrease on subsequent days. Secondly, NMS models will be robust from day to day, hence outperforming machine learning on subsequent days, but would not reach as high performance as CNN models on the first day. Finally, a combination of these two model types in a hybrid model, is expected to incorporate the best of both worlds: reaching as high performance in knee joint torque prediction as CNN models, while being as robust as NMS models.

CNN hyperparameter optimization led to the following architecture: three convolutional layers, with 32 filters and a kernel size of 7 and an LSTM layer with 64 filters. Batch normalization was applied between each layer and a dropout rate of 0.1 was used. For the CNN part of the Hybrid version a similar architecture was used. See also Table 1. An example of the torque predictions by the three different type of models can be seen in Figure 2.

The main goal of this study was to find the most suitable model to predict knee joint torque from EMG, to be used for multi-day control of a prosthetic knee joint in non-weight bearing situations. Three different models were developed and validated on both legs of ten able-bodied subjects, using multi-day measurements. The CNN model had the overall lowest prediction error (9.2 ± 4.4%) and performed significantly better than NMS and Hybrid on all days. To the best of our knowledge, our convolutional neural network was the first of its kind able to successfully predict knee joint torque from EMG input data. Next to that, we implemented state-of-the-art NMS models which showed robustness from day to day. We also successfully combined a convolutional neural network and a Hill-type muscle model to create a Hybrid model, which is also first of its kind. This Hybrid model was able to outperform NMS. This study indicates that convolutional neural networks are a suited approach to be used in knee joint torque estimation over multiple days.

The CNN showed the lowest error on the training day and had an increased error on subsequent days, which was in line with our expectations. However, the increase in error did not continue after day 2 and results showed that the CNN was robust over the other three days, showing no significant differences between day 2, 3 and 7. This is not completely in line with expectations from related work. Convolutional neural networks are known to have robustness issues (Uličnỳ et al., 2016; Ghosh et al., 2018; Arcaini et al., 2020). For example, if electrodes are placed differently on day 2 and MVC values differ from day to day, the EMG envelope images that are created can differ too much from day 1 for the CNN to make a good prediction. This may explain the significant differences between day 1 and all other measurement days. However, our findings show no significant differences between day 2, 3 or 7, thus being robust over days, which contradicts literature. A possible explanation is that the variance in EMG envelopes, and thus the input data for the CNN, within a subject is small enough to be handled by the CNN. Another explanation is that the output of the CNN used in this study is low-pass filtered to smooth any outliers, improving the NRMSE and robustness. Next to that, related work suggested that a black-box machine learning method could predict torque values outside of a physiologically plausible space (Sartori et al., 2018). We were able to develop a CNN model with low-pass filter, which was able to predict torques within a small range of the reference value. This study showed that a CNN model is suited for torque estimation within plausible ranges.

Compared to related work, our study shows similar results for the CNN model. To our knowledge no studies into the performance of knee joint angle or torque prediction over multiple days were conducted, thus only the first day performances could be compared. We observed an average error rate of 5.8 ± 1.6% on day 1, which is comparable with related work. Huang et al. reported an average error of 4.9% and Gautam et al. reported an average error of 8.1% for knee joint angle prediction. Zhang et al. reported an average error of 0.7–6.7% for ankle torque prediction.

The NMS model did not differ significantly over days as expected and is the only model that met our definition of robustness. It was expected that robustness was shown over every measurement day (Durandau et al., 2018; Sartori et al., 2018). Related work showed the model’s ability to predict torque in untrained activities, thereby proving its robustness by their definition (Durandau et al., 2018). Our definition of robustness is different since it refers to time and not the model’s ability to predict untrained activities. To our knowledge, little related work investigated robustness from day to day. Just one study calibrated the NMS model on one day and tested the model the day after, but did not test for between-days variance (Sartori et al., 2018). This study showed that NMS is also robust over multiple days. The error observed on day 2, 3 and 7 by the NMS model was significantly higher than the error of the CNN model, which was not expected. Next to that, the average NRMSE of 14.3 ± 4.2% was slightly higher than observed in related work. Durandau et al. reported an average error of 10–11% and Zhang et al. reported an average error of 2–12%. It could be that the model was too complex for the task that was performed. Furthermore, the activities performed in this study find the physiological boundaries of the knee angle and thus of the muscle parameters, which might cause this model to perform less compared to findings in literature.

The performance of the Hybrid model was midway between the performance of the CNN model and NMS. It was not as robust as NMS and did not reach as high performance as the CNN model, thus it did not meet our expectation. Similar robustness behaviour was found compared to the CNN model: robustness was found over day 2, 3 and 7. This can be explained by the fact that Hybrid and CNN models both make use of a CNN, of which its robustness was explained before. The error overall and on day 1 was significantly lower than that of NMS, thus combining NMS with a CNN can lead to better performing models. A possible explanation is that the muscle activation computed by the CNN is more accurate than the muscle activation calculated by the activation component of the NMS model. The Hybrid model thus uses the best features of both the CNN model and NMS: the CNN is used to find a better relation between EMG and muscle activation, and the NMS components provide information about the underlying process of biomechanical movement.

Compared to related work of Hybrid modelling, we found an average NRMSE of 10.0 ± 1.6% on day 1. As no multi-day studies into knee joint angle or torque prediction based on EMG were performed to our knowledge, we cannot compare the results of the other days to related work. Cimolato et al. (2020) found an average NRMSE of 24.0% with their Hybrid model and Xu et al. (2020) found an average RMSE of 5.8% with their Hybrid approach. The application of Xu et al. was on the upper limb which is different than our application in the lower limb. This might explain the difference in error rate compared with our study as the system that needs to be modelled around the elbow is less complex than around the knee. Our Hybrid approach has an error rate which falls between these two studies.

The findings of this study are promising for the use in a transfemoral prosthesis. The CNN model proves to be the best of three models to be used for knee joint torque estimation. However, future work remains to investigate if this finding extends to an online application with amputees as well. The input of the CNNs were windowed to obtain EMG images, which would introduce a real-time delay of the window size (128 ms) + sampling period (16 ms). Output was filtered by a second order low-pass filter with a cut-off frequency of 1Hz, which would cause an additional real-time delay of 1 sample (16 ms), resulting in a total delay of 160 ms. Therefore, with the intended use in mind, it is essential to test performance of these models in real-time using an actual transfemoral prosthesis, using amputees instead of able-bodied subjects. Futhermore, the sample size of ten subjects is limited and could be extended for a more clear result between the different models. Another limitation of this study is that the influence of the maximum voluntary contractions on the EMG data and model performance have not been investigated. The MVC that was performed for this study cannot be done by a transfemoral amputee. An extension of this study should investigate the use of different MVCs, for instance by using a submaximal contraction to estimate maximum contraction as proposed by Kishimoto et al. (2021) and investigate how different MVCs affect the model performances.

This study provides new insight into what modelling framework performs best in predicting knee joint torque from EMG data during non-weight bearing activities in healthy subjects. Three models (CNN model, neuromusculoskeletal model and a Hybrid model) were designed and tested on multi-day measurements to gain knowledge about the robustness of each model to time-varying parameters. Results indicate that the CNN model performed best compared to the other models (NRMSE 9.2 ± 4.4%) and that the Hybrid model (NRMSE 12.4 ± 3.4%) was able to outperform the neuromusculoskeletal model (NRMSE 14.3 ± 4.2%). The NMS model was the only model that was robust over all days. The CNN model and Hybrid models showed only significant differences in performance between the first day and all other days, a promising finding for the robustness of each model. These results contribute to the development of a direct control scheme for a transfemoral prosthesis by providing a clear comparison of all three modelling frameworks evualated over multiple days.