Muscle activity plays a dominant role in the development, growth, and aging process of the musculoskeletal system. Electrical muscle activity is one of the most commonly adopted parameters to characterize neuromuscular disorders (Smith et al., 2020, Van der Heijden et al., 2009), assess motor ability during exercises (Esposito et al., 2011), and develop rehabilitation systems, e.g. prosthesis (Zabre-Gonzalez et al., 2021). Knee flexors and extensors play an essential role in human mobility (Kim et al., 2023, Manini et al., 2007). Gastrocnemius and soleus are responsible for generating plantarflexion moment during gait (Lenhart et al., 2014). The gastrocnemius is essential during gait for maintaining the balance of human body and kicking off the ground during stance phase. It is, therefore, truly promising to be able to estimate the electrical muscle activity of biceps femoris, gastrocnemius, and soleus, and further expand the estimation approach to clinical treatment or rehabilitation.

Conventionally, electrical muscle activity can be quantified by measuring the action potential generated during muscle contractions using Electromyography (EMG) (Akl et al., 2023, Alibeji et al., 2018, Intiso et al., 1994, Muceli and Farina, 2012, Rehbaum et al., 2012, Spulak et al., 2014, Tamei and Shibata, 2011). In laboratory scenarios, EMG is the most commonly used approach for electrical muscle activity measurement, which can not be a trivial task. Several electrodes must be accurately placed on the skin around the targeted muscles to characterize their behavior. For instance, a total of 10 to 15 electrodes are normally requested to record the dynamics of muscles in the thigh. Moreover, currently most commercial EMG real-time visualization highly rely on specialized built-in software, which can usually be used by the well-trained researchers.

Anatomical subject-specific models have also been developed to estimate muscle activity (Trinler et al., 2018). A physical model of the musculoskeletal system is normally required to solve the equation of motion and further estimate muscle activity. However, the redundancy in the human musculoskeletal system may yield different estimation output while using different control strategies of individual muscles. To overcome the above-mentioned model-based approaches, data-driven methods, i.e. deep learning (DL) and machine learning (ML) models, have been developed to estimate electrical muscle activity. Recent studies have demonstrated the possibility of estimating muscle activity based on joint kinematics and kinetics collected with optical motion capture system (Zabre-Gonzalez et al., 2021) using data-driven methods. However, the estimation process strongly relies on the marker-based optical motion capture and ground reaction force (GRF) measurements using an in-lab system, which dramatically limited its application scenario. In the past few years, the rapid development of wearable sensors, represented by Inertial Measurement Units (IMUs), made it possible to monitor human kinetics using these sensors in daily life. IMUs-based electrical muscle activity estimation approach, as an alternative of EMG, provides a more portable manner for motion analyses during locomotive activities. EMG electrodes can easily fall off during the extensive sports, e.g. volleyball, cycling, or basketball, which can be potentially resolved by IMUs-based method. Previous studies developed DL models to estimate joint moments with as few as single (Liang et al., 2023), two (Stetter et al., 2020, Stetter et al., 2019), four (Dorschky et al., 2020) IMUs, which proves the feasibility of quantifying kinetic parameters using sparse IMUs. However, only few studies have attempted to establish DL models to estimate electrical muscle activity using IMUs-based motion data. An ANN was proposed to estimate the average electrical muscle activity of the rectus femoris and gastrocnemius muscle during gait cycle, the estimation of discrete data was achieved only using two IMUs (Gu et al., 2022). Further, two DL models, namely, feed-forward neural network and LSTM, were proposed to estimate continuous electrical muscle activity during running using four IMUs attached on the trunk, thigh, shank, and foot (Khant et al., 2023). It is therefore indicated that the integration of the DL models and IMUs might be an effective solution of electrical muscle activity estimation during walking and running. Further reducing the number of IMUs sensors and guaranteeing the estimation performance of electrical muscle activity would be one of the most critical steps for expanding the application of IMUs sensors.

In addition, large-scale dataset is normally required for the implementation of DL models and to maintain reasonable accuracy. However, data collection in many clinical applications is normally time-consuming, costly and limited on the number of participants, leading to small sample sizes for DL model development. To overcome the limitation of small sample size, simulated IMUs data was generated from the motion data to augment the labeled dataset for DL model training (Johnson et al., 2021, Molinaro et al., 2022, Mundt et al., 2020). Nevertheless, the performance of the model trained by the simulated IMUs data is still questionable due to the exclusion of environmental interference and moving artifacts contained in real IMUs data. Generative adversarial network (GAN)-based frameworks have been well introduced in the sequential data generation (Donahue et al., 2018, Esteban et al., 2017, Yoon et al., 2019) and are one of the most promising solutions to enlarge the sample size. To our knowledge, GAN-based data augment methods have never been used in either human muscle activity estimation nor the human kinetic parameter estimation.

Speed is a critical determinant of gait patterns. Joint kinetics, joint kinematics, and muscle activations change with gait velocity (Fukuchi et al., 2019). Differences in walking speed have been shown to alter muscle activations (Schwartz et al., 2008, Trinler et al., 2018). Moreover, gait velocity could affect the performance of gait recognition model. A decline performance of a continuous gait-phase recognition algorithm was observed at the untrained speeds (Lu et al., 2022). Likewise, the performance of muscle activity estimation algorithm trained with data at one gait speed might also change when extrapolating to the other gait speeds. Therefore, in the present study, the estimation performance of the proposed model was assessed across three gait speeds, i.e., slow gait, self-selected free gait, and fast gait.

The purpose of the present study was to estimate the EMG envelope during gait using the DL model and augment the small-scale dataset collected form two IMUs using a GAN-based model. To achieve these purposes, a GAN-based data augment method (MuscleGAN) was proposed to overcome the limitation of small sample size. Furthermore, a subject-independent multiple-input multiple-output (MIMO) regression DL model was proposed for EMG envelope estimation. Eventually, the generalization and estimation performance of the regression model were further validated and assessed. The present study is the first attempt to develop a GAN-based data augment method and improve the performance of DL model in the estimation of human kinematic and kinetic parameters. It is also the first attempt to use only two IMUs to estimate the continuous EMG envelope.