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Physics-Informed Neural Networks for Real-Time Muscle-Tendon Force Estimation From Wearable Sensors
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DOI：10.1109/tnsre.2026.3716076.png)
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Abstract
En 中文
Clinicians currently lack practical tools to quantify muscle-tendon forces outside of research laboratories, limiting load-management decisions during rehabilitation to symptom-based progression. This article presents a physics-informed neural network (PINN) framework that estimates individual muscle-tendon forces from wearable inertial measurement units (IMUs) and pressure-sensitive insoles, without requiring labeled force data or electromyography. The framework combines deep neural networks with differentiable rigid-body and Hill-type muscle models, enforcing torque equilibrium and minimizing activation effort to handle muscle redundancy. Validated on 16 subjects during walking, the framework estimated Achilles tendon forces with nRMSE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 8.8\pm 1.5\%$ </tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}^{{2}} = 0.92\pm 0.03$ </tex-math></inline-formula>, matching the performance of supervised methods trained on labeled forces despite using none. Inference times of approximately 7 ms support potential closed-loop biofeedback applications. We further show that the framework can adapt to altered musculoskeletal parameters representing post-rupture Achilles pathology using only physics-based constraints, predicting compensatory recruitment patterns consistent with clinical observations. The proposed approach establishes a computational foundation for translating laboratory-grade biomechanical analysis to wearable systems for continuous rehabilitation monitoring.
Keywords:
Achilles tendon
muscle forces
physics-informed neural networks
rehabilitation monitoring
wearable sensors
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