Joint angle trajectories are Robust to segment length estimation methods in human reaching

Abstract

Background: Quantitative movement analysis is increasingly used to assess motor deficits, but joint angle calculations depend on assumptions about limb segment lengths. These lengths are often estimated from average anthropometric proportions rather than measured directly. The extent to which such assumptions influence joint angle accuracy and variability remains unclear.

Methods: In prior studies, we recorded reaching movements in nine healthy adults using active-marker motion capture system. In this study, we computed arm joint angles with a dynamic model scaled using either measured segment lengths (Individual method) or proportions based on body height (Average method). Each participant served as their own control across two modeling conditions. We compared segment proportions and the variability in joint angle trajectories arising from segment length assumptions (between-participant variability) with within-participant variability across repeated movements.

Results: Segment length proportions remained unchanged despite increases in population height. Joint angle trajectories derived from the two scaling methods were very similar. Segment length assumptions had only minor effects on joint angle amplitudes, primarily due to kinematic redundancy, and these effects were substantially smaller than the within-participant variability observed across repeated movements in most individuals. Importantly, while segment length estimates shifted absolute joint angle amplitudes, they did not alter the shape of angular trajectories.

Conclusions/significance: Morphological variability in segment lengths contributes less to joint angle variability than the variability expressed by individuals across repeated movements. This indicates that movement variability inherent in movement execution outweighs that introduced by morphological differences. These findings suggest that motion capture-based assessments of reaching quality remain accurate even when segment lengths are inferred from height, supporting their practical use in remote or telehealth clinical assessments where direct anthropometry is not feasible.

Fig 1. Illustration of kinematics.

Red segments are 10% shorter each than the black segments. Dashed lines show axes against which the joint angles were measured. E/F stands for extension/flexion degree of freedom of the corresponding joint. A. When the joint angles are kept the same, the changes in limb segment lengths change the location where the hand can reach. Green dots illustrate the locations of markers used for motion capture. B. When the tip of the hand is kept the same, the changes in limb segment lengths change joint angles.

Fig 2. Example of the differences between joint angle trajectories calculated with models scaled in two ways for a single movement in one direction (and back) performed by one participant.

Joint angle trajectories were calculated from musculoskeletal models scaled using average proportions (black) and individual arm segment lengths (red). Thick lines show average trajectories and shaded areas show standard deviation across 15 repetitions for the same movement. Abbreviations: E/F = extension/flexion; Ab/Ad = abduction/adduction; E/I = external/internal; R/U = radial/ulnar.

Fig 3. Statistical parametric mapping analysis of joint angle time series comparing segment length estimation methods.

The black curve represents the one-dimensional statistical parametric mapping (SPM) t-statistic as a function of time. The red dashed line indicates the critical threshold (t*) based on random field theory at α = 0.05. No supra-threshold clusters were identified. Abbreviations: E/F = extension/flexion; Ab/Ad = abduction/adduction; E/I = external/internal; R/U = radial/ulnar.

Fig 4. Comparison between within- and between-participant variability.

Values of between-participant variability (${\mathit{\sigma }}_b$ blue) and within-participant variability (${\mathit{\sigma }}_w$) were averaged across all participants (lines indicate mean values and shaded areas indicate standard deviation across participants) for each target location and degree of freedom. The insert shows the locations of targets 1-14 relative to the participant’s position (drawn not to scale). Abbreviations: E/F = extension/flexion; Ab/Ad = abduction/adduction; E/I = external/internal; R/U = radial/ulnar.