A physiologically constrained musculoskeletal neural network (MSK-NN) is proposed for multi-degree-of-freedom (DoF) joint kinematics estimation from partially observed surface electromyography (sEMG) signals. The framework integrates a neural activation estimator with an embedded musculoskeletal forward dynamics module, trained end-to-end using a composite loss function that combines kinematic supervision, synergy regularization on measured muscles, and anatomy-guided trend regularization on unmeasured muscles.
MSK-NN Framework
The activation estimator and the MSK forward dynamics module are jointly optimized through end-to-end backpropagation with a composite physics-physiology loss that combines kinematic supervision, synergy regularization on measured muscles, and anatomy-guided trend regularization on unmeasured muscles.
Data Acquisition and Processing
The experimental protocol is approved by the University Research Ethics Committee at the University of Manchester (Reference No. 2024-20628-36971). Six healthy subjects participated in the study with written informed consent. Height, body mass, and hand length are recorded before data collection. During the experiment, participants perform wrist movements in a seated position while maintaining a neutral forearm posture and avoiding forearm pronation and supination.
Each participant performs four types of continuous wrist motion patterns without constraints on speed or amplitude: clockwise (CW), counterclockwise (CCW), figure-8 shaped, and random (RND). For each pattern, six 30-second trials are recorded, with the middle 20 seconds retained to remove transient effects.
Raw sEMG signals are band-pass filtered (20–450 Hz, fourth-order Butterworth), rectified, and low-pass filtered (4 Hz, fourth-order Butterworth) to obtain sEMG envelopes. Maximum voluntary contraction (MVC) of each muscle is recorded before the experiment, and the envelopes are normalized by the MVC peak amplitude of each muscle. Processed sEMG envelopes are resampled to 100 Hz to match the kinematic sampling rate.
MSK-NN Training
The preprocessed dataset is split at the trial level into training, validation, and test sets with a 4:1:1 ratio. A subject-specific model is trained using all four motions pooled together, with evaluation conducted separately for each motion type.
Results
The proposed MSK-NN is evaluated from four perspectives. First, its multi-DoF kinematics prediction performance is compared against state-of-the-art deep learning baselines. Second, the inferred input-excluded extensor carpi radialis brevis (ECRB) activation is compared with the recorded ECRB sEMG envelope, which is withheld from the input and used only for physiological plausibility assessment. Third, the optimized MSK parameters are examined against physiological ranges. Finally, a muscle ablation analysis is conducted to assess the contribution of unmeasured muscles to kinematics estimation performance.
Unmeasured Muscle Ablation Analysis
These findings show that including muscles unavailable to the network improves the completeness of the muscle-drive representation and contributes to more accurate multi-DoF wrist kinematics estimation under partial sEMG observability.
Discussion
The proposed MSK-NN framework is discussed from three perspectives: modularity and extensibility, its capability to estimate muscle activations under partially observed sEMG, and its computational feasibility for real-time execution.
Modularity and Extensibility of the Framework
MSK-NN seamlessly integrates two components: a neural activation estimator and an embedded MSK forward dynamics module, coupled only through the muscle activation vector that serves as a well-defined physiological interface between the data-driven and physics-based stages. This compositional structure allows either component to be replaced independently without altering the overall framework.
Computational Feasibility for Real-Time Execution
The proposed MSK-NN is evaluated for single-step model latency at 250 Hz on a laptop equipped with an NVIDIA GeForce RTX 4080 Laptop GPU, an Intel Core i9-13980HX processor, and 32 GB RAM. The CNN-based muscle activation estimator requires 0.55 ms (95th percentile: 0.66 ms), the muscle-tendon dynamics module requires 1.38 ms (95th percentile: 1.60 ms), and the joint dynamics module requires 0.43 ms (95th percentile: 0.51 ms). The total inference computation time per step is 2.65 ms (95th percentile: 3.17 ms). These results indicate that the computational core of MSK-NN is feasible for real-time execution at 250 Hz.
Frequently Asked Questions
How does MSK-NN handle partially observed sEMG signals? The framework uses synergy regularization on measured muscles and anatomy-guided trend regularization on unmeasured muscles to infer missing activations from the observed signals.
What wrist motion patterns were used to evaluate the model? Participants performed four continuous motion patterns: clockwise, counterclockwise, figure-8 shaped, and random, without constraints on speed or amplitude.
Can MSK-NN run in real time on standard hardware? Yes, the total inference time per step is 2.65 ms at 250 Hz on a laptop with an RTX 4080 GPU, well within real-time requirements.
What makes the MSK-NN framework modular and extensible? The neural activation estimator and musculoskeletal forward dynamics module are coupled only through the muscle activation vector, allowing either component to be replaced independently.