Radial coordination variability: The radial vector coding for quantifying movement stability

Traditional modified vector coding (mVC) quantifies spatial segmental coordination using planar coupling angles. However, current approaches lack a method to find which joint couplings most affect task performance. We introduce the radial vector coding rVC, a 3D extension of mVC by transforming joint trajectories from Cartesian to spherical coordinates and defining a novel metric, the radial coordination variability (CV_r) from fluctuations in the radial component over time. This spatially integrated approach captures deviations from steady motion trajectories and reflects dynamic coordination variability. We applied the method to gait data from 42 healthy adults (24 young, 18 older) walking at eight speeds (40-145 % of preferred speed, normalized as a Froude number). Using a spherical coordination transformation, we calculated CV_r for the pelvis, hip, knee, ankle, and foot. In young adults, CV_r increased with speed and was higher at distal joints, indicating adaptive flexibility. Older adults showed the same segmental hierarchy but with a reduced CV_r at the ankle and knee, reflecting more constrained control. Significant joint × speed × age interactions confirmed that CV_r captures both functional coordination and age-related adaptations. This new approach enables efficient, spatially integrated analysis of 3D movement coordination and variability. Compared to traditional mVC, rVC avoids combinative complexity in multi-joint systems, offering a scalable method for coordination analysis across tasks and populations.