⚡ electrical engineering

Physiologically Constrained Musculoskeletal Neural Network for Multi-DoF Joint Kinematics Estimation from Partially Observed sEMG

This paper proposes a novel, fully differentiable Musculoskeletal Neural Network (MSK-NN) that estimates multi-degree-of-freedom joint kinematics from partially observed sEMG by simultaneously inferring unmeasured muscle activations through a composite physics-physiology loss, achieving superior accuracy and physiological plausibility compared to existing deep learning baselines without requiring direct biomechanical supervision.

Original authors: Wending Heng, Mingming Zhang, Glen Cooper, Zhenhong Li

Published 2026-06-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Wending Heng, Mingming Zhang, Glen Cooper, Zhenhong Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Blind" Robot

Imagine you are trying to teach a robot to move a human wrist. Usually, you'd put sensors on every single muscle in the forearm to tell the robot what to do. But in the real world, that's impossible. Some muscles are too deep inside the arm, too small, or just in spots where you can't stick a sensor without it falling off.

This creates a "blind spot." The robot only sees signals from a few muscles (the ones it can measure) but has to guess what the hidden muscles are doing. If the robot guesses wrong, the wrist might move in a way that feels unnatural or physically impossible, like a puppet with tangled strings.

The Solution: MSK-NN (The "Smart Guessing" System)

The authors created a new computer program called MSK-NN. Think of it as a two-part team working together to solve the puzzle:

The "Detective" (The Neural Network): This part looks at the signals from the muscles it can see. It's like a detective looking at footprints at a crime scene. It tries to guess what the hidden muscles are doing based on the clues it has.
The "Physics Coach" (The Musculoskeletal Model): This is the secret sauce. Instead of just guessing, the Detective runs its ideas through a strict "Physics Coach." This Coach knows the rules of human anatomy and physics (like how muscles pull on bones and how joints rotate). If the Detective guesses that a muscle is pulling in a way that would break a bone or defy gravity, the Coach says, "Nope, try again."

How They Train the Team

Usually, to teach a computer to understand muscles, you need to know the exact force every muscle is generating. But measuring that force inside a living human is incredibly hard and expensive.

The authors got around this by using a three-part rulebook (a "loss function") to train the system without needing those hard-to-get force measurements:

The "Target Score" (Kinematics Loss): Did the wrist move to the right angle? If the robot's guess results in the wrong wrist position, it gets a penalty.
The "Teamwork Rule" (Synergy Loss): Muscles don't work alone; they work in groups (like a rowing team). The system checks if the visible muscles are working together in a natural, coordinated pattern. If they are acting weirdly out of sync, it gets a penalty.
The "Family Resemblance" Rule (Trend Loss): This is the clever part for the hidden muscles. The system knows that certain deep muscles usually work in sync with specific surface muscles. Even though it can't see the deep muscle, it forces the deep muscle's "guess" to move in time with its visible "cousin." If they don't move together, it gets a penalty.

The Experiment: The Wrist Workout

The team tested this on human wrists. They asked people to move their wrists in four ways:

Clockwise circles.
Counter-clockwise circles.
Figure-8s.
Random, chaotic movements (the hardest test).

They compared their new system against other popular AI methods (like standard neural networks or LSTM models).

The Results: Why It Won

Better Accuracy: The MSK-NN system predicted the wrist movement much more accurately than the others, especially during the random, chaotic movements. The other systems tended to get confused and jittery when the motion wasn't a perfect circle.
The "Magic" Guess: The system was tested on a specific deep muscle (called APL) that was never shown to the computer. The system had to guess its activity entirely on its own. When they compared the computer's guess to the actual hidden muscle's signal (which they recorded secretly just for checking), the guess was remarkably accurate. It proved the system could "see" the invisible muscles.
Physically Real: The numbers the system came up with for muscle strength and length stayed within the limits of what is biologically possible for a human. It didn't invent super-human muscles.

The "Ablation" Test (What happens if we remove parts?)

The researchers did a "what-if" experiment. They turned off the part of the system that guesses the hidden muscles.

Result: The accuracy dropped.
Meaning: This proved that guessing what the hidden muscles are doing is actually necessary. You can't just ignore the deep muscles and expect the wrist to move correctly.

The Bottom Line

This paper presents a new way to teach computers to understand human movement when they can't see all the muscles. By combining a smart AI guesser with a strict physics coach, the system can predict how a wrist will move and even "hallucinate" (accurately guess) the activity of muscles it can't see. It works better than current methods, especially when movements are unpredictable, and it stays true to the laws of human biology.

Technical Summary: Physiologically Constrained Musculoskeletal Neural Network for Multi-DoF Joint Kinematics Estimation

Problem Statement
Surface electromyography (sEMG)-based continuous joint kinematics estimation is critical for rehabilitation, biomechanics, and human-robot interaction. However, existing approaches face a trade-off between accuracy and physiological interpretability. Model-free data-driven methods (e.g., CNNs, LSTMs) often lack physiological consistency and fail to generalize to movement patterns with speeds or amplitudes unseen during training. Conversely, model-based approaches explicitly represent musculoskeletal (MSK) forward dynamics but are limited by model fidelity and the inability to account for unmeasured muscles (e.g., deep or small muscles inaccessible to sensors). Furthermore, existing hybrid frameworks often require expensive biomechanical labels (e.g., muscle-tendon forces or joint torques) for supervision or assume a strict one-to-one mapping between sEMG channels and modeled muscles, which excludes unmeasured task-relevant muscles and leads to physiologically implausible force sharing.

This paper addresses the challenge of estimating multi-degree-of-freedom (DoF) joint kinematics under partially observed sEMG, where a subset of task-relevant muscles cannot be measured due to anatomical constraints or sensor limitations.

Methodology
The authors propose a Musculoskeletal Neural Network (MSK-NN), a fully differentiable architecture that integrates a data-driven activation estimator with an embedded MSK forward dynamics module.

Architecture:
- Muscle Activation Estimator: A lightweight Convolutional Neural Network (CNN) encoder processes pre-processed sEMG envelopes from measured muscles. Unlike conventional approaches, this encoder jointly estimates activations for both the measured muscles and the unmeasured (latent) muscles.
- Embedded MSK Forward Dynamics: The estimated activations are propagated through a Hill-based muscle-tendon dynamics model to generate muscle forces. These forces are mapped to joint torques via moment arms and integrated within a subject-specific joint dynamics model (inertia, gravity, and damping) to predict multi-DoF joint angles.
Training and Loss Function:
The network is trained end-to-end without direct supervision of internal biomechanical variables (e.g., forces or torques). Instead, a composite Physics-Physiology Loss is designed to constrain the solution space:
- Joint Kinematics Loss ( $L_{traj}$ ): Penalizes discrepancies between predicted and ground-truth joint angles and angular velocities.
- Muscle Synergy Loss ( $L_{syn}$ ): Uses Non-Negative Matrix Factorization (NMF) derived from training data to constrain the activations of measured muscles to lie within a physiologically plausible coordination subspace.
- Anatomy-Guided Trend Loss ( $L_{trd}$ ): Encourages temporal coordination between unmeasured muscles and functionally related measured muscles. This loss minimizes the difference in activation trends (temporal derivatives) between paired muscles, transferring coordination structure from observed to unobserved muscles.
Optimization:
Both the CNN encoder weights and the parameters of the Hill-based muscle-tendon dynamics (e.g., optimal fiber length, maximum isometric force) are optimized simultaneously via backpropagation, allowing for subject-specific personalization of the MSK model.

Key Contributions

Novel Framework: Introduction of MSK-NN, which estimates multi-DoF kinematics while inferring physiologically plausible activations for both measured and unmeasured muscles without requiring a one-to-one sEMG-to-muscle mapping.
Supervision-Free Internal Variables: The method achieves high kinematic accuracy without requiring expensive biomechanical labels (forces/torques) for training, relying instead on a composite loss function that enforces physical and physiological consistency.
Handling Partial Observability: The framework explicitly models unmeasured muscles (e.g., deep muscles like the Abductor Pollicis Longus) and infers their activations, addressing the "incomplete muscle-drive" problem common in traditional model-based approaches.

Experimental Results
The method was evaluated on two-DoF wrist kinematics (Flexion/Extension and Radial/Ulnar Deviation) using data from six healthy subjects performing four motion types: Clockwise (CW), Counter-Clockwise (CCW), Figure-8 ( $\infty$ -shaped), and Random (RND) motions.

Kinematic Accuracy: MSK-NN outperformed state-of-the-art baselines (CNN, Bi-LSTM, CNN-LSTM, and Parallel Efficient Transformer (PET)) in Normalized Root Mean Square Error (NRMSE) and Coefficient of Determination ( $R^2$ ). The performance gap was most significant in the Random Motion (RND) condition, demonstrating superior generalizability to unseen movement patterns.
Physiological Plausibility: The estimated activation of an input-excluded muscle (ECRB) showed strong temporal agreement (high Pearson and Spearman correlation coefficients) with its recorded sEMG envelope, validating the network's ability to infer latent activations.
Parameter Validity: Optimized MSK parameters remained within established physiological limits, confirming the model's ability to learn subject-specific dynamics without violating biomechanical constraints.
Ablation Study: Progressive removal of unmeasured muscles (APL and ECRB) from the model resulted in significant performance degradation, particularly in the RUD DoF and complex motions, confirming the critical role of modeling unobserved muscles.

Significance and Claims
The paper claims that MSK-NN provides a robust solution for joint kinematics estimation under sparse sensing conditions. By embedding physics directly into the network architecture and utilizing a composite loss function, the method achieves a balance between the accuracy of data-driven models and the interpretability of model-based approaches.

Crucially, the authors state that MSK-NN:

Generalizes better to random, unconstrained motions compared to existing hybrid and data-driven baselines.
Recovers physiologically plausible activations for muscles not present in the input, effectively solving the underdetermined nature of partial sEMG observation.
Offers a general template for coupling data-driven estimation with physiologically constrained dynamics, potentially supporting studies of neuromuscular control under unseen motions and providing interpretable intermediate variables for scientific and engineering applications.

The authors modestly note that while the framework is computationally feasible for real-time execution (approx. 2.65 ms per step), its primary contribution lies in the architectural design and the demonstrated capability to infer latent physiological states without direct supervision.