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

Musculoskeletal models have been widely used for detailed biomechanical analysis to characterise various functional impairments given their ability to estimate movement variables (i.e., muscle forces and joint moments) which cannot be readily measured in vivo. Physics-based computational neuromusculoskeletal models can interpret the dynamic interaction between neural drive to muscles, muscle dynamics, body and joint kinematics and kinetics. Still, such set of solutions suffers from slowness, especially for the complex models, hindering the utility in real-time applications. In recent years, data-driven methods have emerged as a promising alternative due to the benefits in speedy and simple implementation, but they cannot reflect the underlying neuromechanical processes. This paper proposes a physics-informed deep learning framework for musculoskeletal modelling, where physics-based domain knowledge is brought into the data-driven model as soft constraints to penalise/regularise the data-driven model. We use the synchronous muscle forces and joint kinematics prediction from surface electromyogram (sEMG) as the exemplar to illustrate the proposed framework. Convolutional neural network (CNN) is employed as the deep neural network to implement the proposed framework. Simultaneously, the physics law between muscle forces and joint kinematics is used the soft constraint. Experimental validations on two groups of data, including one benchmark dataset and one self-collected dataset from six healthy subjects, are performed. The experimental results demonstrate the effectiveness and robustness of the proposed framework.