Hand Trajectory Arc-Length for Robust Alignment: Reparameterization and Landmark-Based Approaches in Upper Limb Assessment After Stroke

Purpose : Quantitative assessment of upper limb function in individuals who have had a stroke requires analysis of kinematic and kinetic data collected during the execution of daily living tasks. In clinical practice, representative average curves of joint angles and moments are essential for accurately evaluating individual performance and monitoring functional recovery. However, the inherently non-periodic nature of these functional tasks, combined with variable execution speeds both within and across repeated trials, poses a significant challenge for generating such curves. Conventional approaches often fail to properly align the different phases of movement, resulting in inaccurate or misleading average profiles. Methods : To overcome these limitations, two distinct techniques are proposed. The first involves curve registration through landmark-based alignment, a widely accepted nonlinear method for reducing intra-subject variance. However, this procedure involves temporal warping, which can alter the original timing of movement phases and may impact the interpretability of the results. The second method relies on a time-independent parameterization using the arc-length of the hand trajectory, which naturally aligns signals by reparameterizing each movement according to the distance traveled by the hand. Results : Both methodologies are applied to the hand-to-mouth task in individuals with a stroke. Although conceptually different, the two approaches yield similar average curves when reference points are defined as equidistant points along the temporal evolution of the hand trajectory arc length. Conclusions : By applying these methods, realistic average curves of joint angles and moments are obtained, which are essential for improving rehabilitation protocols and assessing functional recovery in post-stroke individuals.