Physics-Informed Neural Networks for Real-Time Muscle-Tendon Force Estimation from Wearable Sensors

Kárason H, Ritrovato P, Maffulli N, Tortorella F (2026)

Publication Type: Journal article

Publication year: 2026

Journal

IEEE Transactions on Neural Systems and Rehabilitation Engineering Institute of Electrical and Electronics Engineers (IEEE)

DOI: 10.1109/TNSRE.2026.3716076

Abstract

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 electromyo-graphy. 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 = 8.8±1.5%, R2 = 0.92±0.03, 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.

Involved external institutions

Università degli Studi di Salerno IT Italy (IT) Università degli studi "La Sapienza" IT Italy (IT)

How to cite

APA:

Kárason, H., Ritrovato, P., Maffulli, N., & Tortorella, F. (2026). Physics-Informed Neural Networks for Real-Time Muscle-Tendon Force Estimation from Wearable Sensors. IEEE Transactions on Neural Systems and Rehabilitation Engineering. https://doi.org/10.1109/TNSRE.2026.3716076

MLA:

Kárason, Halldór, et al. "Physics-Informed Neural Networks for Real-Time Muscle-Tendon Force Estimation from Wearable Sensors." IEEE Transactions on Neural Systems and Rehabilitation Engineering (2026).

BibTeX: Download