Technical evaluation of transport-derived movement trajectories during knee osteoarthritis rehabilitation

Abstract

Wearable inertial sensors enable repeated movement recording during knee osteoarthritis rehabilitation, but methods for summarizing multivariable changes across routine sessions remain exploratory. This retrospective technical evaluation examined a normalized transport-derived deviation (NTD) constructed from paired shank-mounted inertial measurement units. Seven participants contributed 46 paired-sensor sessions over 45 d. An approximately 30 s active movement segment from each session was divided into 13 windows and represented using 58 time-domain, frequency-domain and cross-sensor features. Session distributions were compared with each participant’s first usable sensor session using an archived entropically regularized transport implementation. The output was normalized by the baseline-to-final-session value. Mean NTD values at the scheduled assessment days were 0.00, 0.02, 0.23, 0.63 and 1.00. 14 of the 46 displayed values were structurally constrained baseline or final values; no monotonic constraint was applied to the 32 interior observations, which formed non-decreasing trajectories. At interior scheduled days 5, 15 and 30, absolute differences between mean NTD and participant-adjusted normalized elapsed time were 0.057, 0.076 and 0.019. 21 of the 46 archived calculations reached the 500-iteration limit without meeting the 1 × 10−6 residual criterion. A log-domain stabilized recomputation of all 46 primary comparisons satisfied a 1 × 10−8 criterion, with a mean absolute archived-to-stabilized NTD difference of 0.004 (maximum 0.018) across the 32 interior observations. Across support-point counts of 100–1000, interior archived NTD values changed by 0.009–0.026 on average. Routine paired-shank recordings were organized into ordered longitudinal trajectories and the resulting trajectory structure was numerically reproducible under the evaluated implementation. NTD should presently be interpreted as an implementation-specific retrospective coordinate rather than a validated rehabilitation outcome. By defining the requirements for standardized movement tasks, prospective normalization and reproducible sensor placement, these findings provide a practical foundation for prospective validation of transport-based rehabilitation assessment.