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

Jie Zhang, Yihui Zhao+5 more|White Rose Research Online (University of Leeds, The University of Sheffield, University of York)|Jul 4, 2022

Muscle activation and electromyography studies22 citations

TL;DR

A physics-informed CNN framework predicts muscle forces and joint angles from surface EMG by embedding musculoskeletal physics as soft constraints in the loss function, validated on knee and wrist datasets.

ABSTRACT

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 moment) 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 has 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. At the same time, 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.

Motivation & Objective

• Motivate fast, accurate musculoskeletal predictions by combining physics-based neuromuscular knowledge with data-driven learning.
• Develop a CNN-based framework that maps EMG signals to muscle forces and joint kinematics.
• Incorporate physics laws relating muscle forces to joint motion as soft constraints in training.
• Demonstrate robustness and generalization on benchmark walking and wrist motion datasets.

Proposed method

• Use a CNN to map time-series EMG and time steps to muscle forces and joint angles.
• Formulate a total loss as L_total = L_F + L_θ + L_P where L_F and L_θ are MSE losses for forces and angles, and L_P enforces physics-based motion equations.
• L_P is derived from M(θ)θ¨ + C(θ,θ˙) + G(θ) = τ, with τ = Σ r_n F^n_t, penalizing deviations from Newton-Euler dynamics.
• Architect a lightweight CNN: one conv block, two fully connected blocks, and a regression block; training with SGD, batch size 1, 1200 iterations, learning rate 0.01, dropout 0.3.
• Demonstrate flexibility to replace CNN with other architectures (LSTM, GAN) and add more physics constraints (Hill model, activation dynamics).
• Evaluate with RMSE and Pearson CC on knee and wrist datasets, comparing to CNN, ML-ELM, ELM, and SVR.

Experimental results

Research questions

• RQ1 Can a physics-informed CNN accurately predict muscle forces and joint kinematics from surface EMG.
• RQ2 Does embedding physics as a soft constraint improve robustness and generalization compared to purely data-driven models?
• RQ3 How does the framework perform on knee and wrist movements across different subjects and sessions?
• RQ4 What is the impact of training data size on performance when physics constraints are included?
• RQ5 How flexible is the framework to other neural architectures and additional physics laws?

Key findings

• The proposed physics-informed CNN achieves lower RMSE and higher CC than baseline methods across knee and wrist cases in most subjects.
• Embedding physics constraints improves robustness and reduces overfitting, enabling good performance with smaller training datasets.
• The framework with a simpler network sometimes matches or exceeds the performance of deeper CNN baselines, demonstrating the benefit of physics-based regularization.
• In intrasession scenarios, the framework remains more robust than most baselines as walking speeds vary.
• Training data size affects all models, but the physics-informed approach shows faster convergence and better performance with fewer samples.