Source-linked AI summary
Physics-informed Deep Learning for Musculoskeletal Modelling: Predicting Muscle Forces and Joint Kinematics from Surface EMG
Jie Zhang, Yihui Zhao, Fergus Shone, Zhenhong Li, Alejandro F. Frangi, Shengquan Xie, Zhiqiang Zhang
TL;DR
Physics-based musculoskeletal models are slow, while data-driven models lack explicit neuromechanical mechanisms. This paper embeds physics-based soft constraints into a CNN that predicts muscle forces and joint kinematics from sEMG, with experiments reporting robust performance across datasets and conditions. The framework was evaluated only on simple one-DoF wrist and knee movements.
Problem
Physics-based models can be slow, whereas data-driven models do not explicitly reflect underlying neuromechanical processes.
Method
The framework embeds physics-based domain knowledge as soft constraints in a CNN loss function for predicting muscle forces and joint kinematics from sEMG.
Results
The proposed framework achieves robust predictions across benchmark and self-collected datasets, with lower RMSEs and higher Pearson correlation coefficients in most cases than baseline methods.
Takeaways & Limitations
Embedding physical interactions enables a simpler neural network to achieve comparable performance to a more complex pure CNN while reducing training-data requirements for a given performance.
Takeaways & Limitations
Evaluation was limited to simple one-DoF wrist and knee flexion-extension movements; more complex multi-DoF scenarios remain for future evaluation.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
Physics-based musculoskeletal models capture neuromechanical interactions and estimate otherwise difficult-to-measure movement variables, but they can be slow and redundant. Data-driven models improve speed yet lack explicit representation of underlying physical mechanisms, motivating a physics-informed framework.
- Motivation: Physics-based models can estimate movement variables that are difficult to measure directly and support biomechanical applications such as rehabilitation evaluation and surgical planning.
- Motivation: Physics-based musculoskeletal models interpret interactions among neural excitation, muscle dynamics, and joint kinematics and kinetics.They use recordings such as EMGs, ground reaction forces, and body kinematics to estimate physiological quantities including muscle forces and joint moments.
- Related approaches: Data-driven models offer fast inference by learning mappings between neuromuscular signals and movement variables.Their forward-pass inference is computationally inexpensive even when training is lengthy.
- Related approaches: Data-driven models remain black-box tools because they lack explicit physics modelling of the underlying neuromechanical processes.
- Proposed framework: The proposed framework embeds physics-based domain knowledge as soft constraints in a CNN loss function to predict muscle forces and joint kinematics from EMGs.The framework is validated using benchmark walking data and a self-collected wrist-motion dataset.
A. Physics-informed Deep Learning Framework
The framework combines a CNN data-driven component with a physics-based component linking predicted joint motion and muscle forces. CNN predictions are regularised by physical consistency through a loss function that combines data error and physics-based penalties.
- Framework: CNN receives time steps and EMG signals and outputs predicted muscle forces and joint angles.The outputs are indexed over muscles n = 1, . . . , N and time steps t = 1, . . . , T.
- Framework: The physics-based component represents the physical relationship between joint motion and muscle forces.Predictions from the CNN are required to satisfy the physical equation of motion.
- CNN implementation: A simple CNN architecture is used to implement the framework, consisting of one convolutional block, two fully connected blocks, and one regression block.
- CNN implementation: CNN training uses stochastic gradient descent with momentum, batch size 1, maximum iteration 1200, and initial learning rate 0.01.Each dropout layer uses a dropout rate of 0.3.
- Loss design: The proposed loss combines MSE terms with a physics-based loss that preserves physical constraints during movement.The physics term penalises or regularises the deep neural network loss through a function of predicted variables.
1) MSE Loss:
The MSE loss measures prediction error for muscle forces and joint angles by comparing network outputs with corresponding ground-truth values over time and across muscles.
- MSE Loss: MSE loss compares predicted muscle forces and joint angles with their corresponding ground-truth values.
- MSE Loss: Muscle-force MSE averages squared prediction errors over T time steps and N muscles.
2) Physics-based Loss:
The physics-based loss converts governing musculoskeletal relationships into training constraints. It uses the equation of motion and muscle-generated torque to regularise CNN predictions and support robustness and generalisation.
- Physics-based Loss: The physics-based loss uses the equation of motion to impose constraints on predicted muscle forces and joint kinematics during CNN training.
- Physics-based Loss: The equation of motion includes mass, centrifugal and Coriolis, and gravity terms, together with joint torque.
- Physics-based Loss: Joint torque is calculated by summing each muscle’s moment arm multiplied by its muscle force.The moment arm r_n is exported from OpenSim.
- Physics-based Loss: The physics-based term regularises the data-driven loss and is intended to enhance robustness and generalisation when training data are limited.
III. MATERIAL AND EXPERIMENTAL METHODS
The study evaluates the framework on a benchmark walking dataset and a self-collected wrist-motion dataset, using OpenSim-derived kinematics and muscle forces alongside processed EMG signals.
- Datasets and participants: Two datasets comprise walking trials and self-collected wrist motions from six able-bodied subjects.The walking data were retrieved from a real-world simulation, while the wrist experiment recruited six subjects.
- Walking dataset: Walking trials were processed with OpenSim to compute joint kinematics, torque, and muscle forces while following measured EMGs.Each gait cycle was normalized into 100 frames.
- Data representation: Each walking trial was represented as a 100-by-7 matrix containing time, gait cycle, enveloped EMG signals, and BFS and RF muscle forces.
- Wrist dataset: Wrist motions were recorded with VICON under controlled shoulder and elbow positions, with joint kinematics computed from marker data.Participants maintained a straight torso with a 90° abducted shoulder and 90° flexed elbow.
- Signal processing and data format: Wrist EMG signals were band-pass filtered, rectified, low-pass filtered, and normalized to maximum voluntary contraction.The processed signals were combined with wrist muscle forces and joint angles in trial matrices.
C. Baseline Methods and Parameters Setting
The evaluation compares the proposed framework with CNN, ML-ELM, SVR, and ELM, using RMSE and Pearson correlation coefficient to assess prediction quality.
- Baseline methods: CNN, ML-ELM, SVR, and ELM are used as baseline methods for evaluating the proposed framework.The CNN baseline uses three convolutional blocks, three fully connected blocks, and one regression block.
- Parameter settings: CNN training uses stochastic gradient descent with momentum, batch size 1, maximum 1200 iterations, and initial learning rate 0.01.
- Parameter settings: ML-ELM has five hidden layers, with hidden-node counts selected by grid search, whereas ELM uses one sigmoid-activated hidden layer.
- Evaluation criteria: RMSE measures amplitude discrepancies between estimated variables and ground truth, with y_t and ŷ_t denoting ground-truth and predicted values.
- Evaluation criteria: Pearson’s correlation coefficient is employed as an additional evaluation metric for comparing predicted and ground-truth variables.The supplied passages identify the metric but do not provide its complete displayed formulation.
IV. RESULTS
The proposed framework converges during training and tracks joint angles and muscle forces well across knee and wrist scenarios. Quantitative comparisons report stronger performance than the evaluated baselines in most cases.
- A. Training Process of the Proposed Framework: The wrist total loss becomes very low after 200 iterations and converges after 600 iterations, with small local oscillations.The authors associate the oscillations with batch size 1 and report the same convergence process for the knee case.
- B. Overall Comparisons: Representative knee and wrist predictions fit ground truths well for joint angles and the reported muscle forces.The knee outputs include knee angle, BFS force, and RF force; wrist outputs include wrist angle and five muscle forces.
- B. Overall Comparisons: The proposed framework achieves smaller RMSEs and higher Pearson correlation coefficients in most cases across detailed subject comparisons.These comparisons use results reported in Tables I and II.
- B. Overall Comparisons: Deep learning methods, including the proposed framework, CNN, and ML-ELM, outperform SVR and ELM in predicted performance.The passage attributes this pattern to automatic extraction of high-level features from collected data.
- B. Overall Comparisons: The proposed framework achieves satisfactory performance with lower standard deviations and smaller fluctuations in average RMSE comparisons.With a simple neural-network architecture, it achieves performance comparable to pure CNN.
C. Evaluation of Intrasession Scenario
The proposed framework was evaluated in an intrasession setting using data pooled across walking speeds. It outperformed most baselines and was less affected by walking-speed variation.
- The intrasession evaluation fused data from different walking speeds, using 80% for training and 20% for testing per subject.
- The proposed framework outperformed most baseline methods in the intrasession scenario.
- The proposed framework was not affected by walking speeds, whereas some baseline predictions degraded.SVR’s RF muscle-force performance was better than ELM in Fig. 5(a) but became worse in the intrasession scenario.
V. DISCUSSIONS AND FUTURE DIRECTIONS
The discussion examines training-data requirements and attributes improved efficiency to embedding physics-based knowledge in the CNN loss function. The framework achieved lower errors with fewer samples and converged faster.
- A. Effects of Training Dataset Sizes on Performance: The proposed framework achieved lower normalised RMSEs with fewer training samples than baseline methods.
- A. Effects of Training Dataset Sizes on Performance: The proposed framework was less sensitive to training dataset size as the number of training samples varied.
- A. Effects of Training Dataset Sizes on Performance: Embedding physics-based domain knowledge as a loss penalisation or regularisation term yielded faster convergence and reduced training-data requirements for a given performance.
B. Flexibility of the Proposed Framework
The framework is presented as a flexible paradigm for combining data-driven models with mechanistic musculoskeletal constraints. Experiments indicate that its gains persist with simpler or matched CNN architectures and across configurable components and constraints.
- The framework is a generic paradigm for incorporating mechanistic musculoskeletal constraints, illustrated through joint-angle and muscle-force prediction.
- The proposed framework achieved comparable RMSEs to pure CNN despite using a simpler CNN architecture, while outperforming ML-ELM, ELM, and SVR more stably.
- The framework showed faster convergence with simpler neural-network architecture as training-dataset size increased in the wrist-joint case.
- With identical CNN architectures, the proposed framework achieved better prediction performance than pure CNN.
- The framework components can be withdrawn, adjusted, or replaced, and additional mechanistic constraints can be incorporated for application-specific demands.Examples include replacing the data-driven network, adding a Hill muscle model, and imposing kinetic, activation, or contraction dynamics constraints.
C. Understanding Physics-informed Data-driven Methods for Musculoskeletal Modelling
Physics-informed data-driven modelling integrates physics-based knowledge as soft constraints to address the limited interpretability and robustness of conventional machine-learning approaches. The framework also targets reduced model-building effort, while its evaluation remains limited to simple one-degree-of-freedom movements.
- Data-driven models are fast and intuitive but may violate musculoskeletal physics, reducing robustness, generalisation, and interpretability.Their predictions can fit kinematic measurements during training without satisfying the associated biomechanics.
- Evaluation covered only simple one-degree-of-freedom wrist and knee flexion-extension movements, leaving more complex multi-degree-of-freedom scenarios for future work.The authors state that reliability and accuracy will be evaluated in such more complex scenarios.
- Personalised information can be embedded into the framework to reduce manual intervention and accelerate semi-automated model building.Personalised musculoskeletal models support medical procedures, subject-specific robotic devices, and human-machine interfaces, but currently require time-consuming and costly geometry interpretation.
- The proposed framework embeds physics-based domain knowledge as soft constraints that penalise or regularise the deep neural network loss function.This knowledge-embedding design is presented as a general paradigm for musculoskeletal modelling.
- Experiments on two data groups indicate feasibility, while the framework is reported to improve robustness and generalisation and reduce computational demands in model building.The authors position the methodology as potentially applicable to muscle-force prediction and other musculoskeletal-modelling applications.