Physics-Informed Deep Learning for Musculoskeletal Modeling: Predicting Muscle Forces and Joint Kinematics from Surface EMG

Computer Science Engineering Medical Laboratory Science Electrical Engineering Information Science Artificial Intelligence Automation Orthopedics Medical Imaging Life Sciences Medicine Bioengineering
physics-informed deep learning musculoskeletal modeling EMG muscle forces joint kinematics

Musculoskeletal models have been widely used in biomechanical analysis because they can estimate motion variables that are difficult to measure directly in living organisms, such as muscle forces and joint moments. Traditional physics-driven computational musculoskeletal models can explain the dynamic interactions between neural inputs to muscles, muscle dynamics, and body and joint kinematics and dynamics. However, these models run slowly due to their complexity, making real-time applications difficult to achieve. In recent years, data-driven methods have emerged as promising alternatives due to their fast implementation and ease of operation, but they fail to reflect the underlying neuro-mechanical processes.

This paper proposes a physics-informed deep learning framework for musculoskeletal modeling. In this framework, knowledge from the field of physics is introduced into data-driven models as soft constraints for penalization/regularization. The paper uses surface electromyography (SEMG) to simultaneously predict muscle forces and joint kinematics as an example, employs convolutional neural networks (CNN) to implement the framework, and conducts experimental validation on two datasets to demonstrate the effectiveness and robustness of the framework.

Paper Source

This paper was co-authored by Jie Zhang, Yihui Zhao, Fergus Shone, Zhenhong Li, Alejandro F. Frangi, Sheng Quan Xie, and Zhi-Qiang Zhang from the School of Electronic and Electrical Engineering and the School of Computing at the University of Leeds, and the Department of Electrical Engineering at KU Leuven. The study was published in the IEEE Transactions on Neural Systems and Rehabilitation Engineering, Issue 31, 2023.

Research Process

Overview of Research Methods

The study develops a physics-informed deep learning framework for the simultaneous prediction of muscle forces and joint kinematics. Convolutional neural networks (CNN) are used as the carrier for deep neural network implementation, with physical laws considered as soft constraints for regularizing the CNN.

Data Processing

  1. Data Preprocessing: Includes band-pass filtering (20Hz to 450Hz), full-wave rectification, and low-pass filtering (6Hz) of the electromyography (EMG) signals recorded during experiments.

  2. Datasets: Two datasets were used in the paper: a benchmark walking dataset and a self-collected wrist joint movement dataset. The former includes data from six healthy volunteers at different walking speeds, while the latter includes data from six healthy volunteers during wrist flexion/extension movements.

  3. Experimental Records: Standardization steps include scaling the musculoskeletal model of each subject using the OpenSim software and calculating joint kinematics axes and muscle activations consistent with the measured EMG signals using inverse kinematics tools. Each gait cycle is standardized into 100 frames.

Experimental Validation

The experimental data include walking trials and wrist movement data. Each trial consists of the time steps in the gait cycle, traversal signals, and muscle forces from the BFS and RF muscles.

Experimental Data Processing Steps

  1. Markers and Muscle Force Data: Joint kinematic axes and joint moments are calculated using inverse kinematics and inverse dynamics tools, and muscle activations are ensured to be consistent with the measured EMG signals using computational muscle control tools.

  2. Algorithm Design: A simple CNN architecture comprising convolutional blocks, fully connected blocks, and regression blocks is used to implement the data-driven model for automatic feature extraction from EMG signals and time steps.

Loss Function Design

  1. Mean Squared Error Loss (MSE): Minimizes the mean squared error between actual values and predicted values.

  2. Physical Loss: Uses motion equations as regularization terms, matching predicted values with physical equation constraints through the loss function.

  3. Total Loss Function: Combines traditional mean squared error loss and physical loss to define the total loss function for model training.

Results

The experimental results show that the proposed physics-informed deep learning framework exhibits superior predictive performance and robustness across different datasets. Compared to baseline methods such as CNN, ML-ELM, SVR, and ELM, the framework offers lower predictive errors and higher correlation coefficients.

Key Results

  1. Knee Joint and Wrist Joint Datasets: The framework demonstrates good dynamic tracking capabilities in both knee and wrist scenarios, achieving robust and efficient predictive results with a small amount of training data.

  2. Statistical Analysis: One-way ANOVA validates the robustness of the framework, showing optimal performance in most cases.

  3. Cross-Session Scenarios: The proposed framework also shows good generalization performance on unknown data.

Training Process

  1. Iterative Process: During training, the total loss shows a decreasing trend as the number of iterations increases, indicating model convergence.

  2. Impact of Dataset Size and Architecture: Larger datasets and appropriately complex network architectures can further enhance model performance.

Discussion and Future Directions

The study’s proposed physics-driven deep learning framework demonstrates the effectiveness of incorporating physical laws in musculoskeletal model predictions. The framework not only applies to existing muscle force and joint kinematics predictions but can also be extended to other musculoskeletal modeling applications such as robot-assisted rehabilitation and sports pathology diagnosis. Furthermore, future work could explore the impact of different loss weights, input-output settings, and additional physical constraints on model performance.

Conclusion

This paper introduces a physics-informed data-driven framework that significantly reduces computational resource demands for model building. Experimental results demonstrate the effectiveness and robustness of this approach in predicting muscle forces and joint angles. In the future, this framework is expected to play an important role in other applications of musculoskeletal modeling, bridging the gap between laboratory prototypes and clinical applications.