Assessment of shoulder functional movements through inertial measurement units for tele-rehabilitation: a quaternion-based approach.

Telerehabilitation improves accessibility and accelerates recovery: in this context, Inertial Measurement Units (IMUs) are promising wearable sensors for remote movement data collection, which allows to evaluate how closely exercise repetitions align with a prescribed trajectory. Current data processing methods for this purpose include data-driven approaches, requiring exercise-specific training through large amount of data, or distance-based methods with unbounded output, not easy to interpret. This study proposes a novel algorithm which combines the versatility of a bounded output score with numerical stability of quaternions. Data from an IMU-based device were acquired during the execution of human functional shoulder movements by both a young and elderly group of participants. Outputs from the application of the proposed methodology on collected data from same or different movements were statistically compared, revealing ability of discriminating repetitions of the same or of different movements ( $p<0.01$ , rrb effect size = 0.97, contrast ratio 1.7). The proposed algorithm was also confronted with the traditional approaches by statistically comparing outputs from comparison matrices rescaled in equal range of values, and results indicated mild differences in performance (rrb effect size < 0.5). Future works may involve integrating this approach into a functioning telerehabilitation system and obtaining feedback on the usability from real users.