Recommendation for the minimum number of steps to analyze when performing the uncontrolled manifold analysis on walking data

Abstract

The uncontrolled manifold (UCM) analysis quantifies the extent to which co-variation among a set of variables facilitates consistent performance by partitioning variance in those variables into two components then calculating their normalized difference (i.e., the synergy index). Although UCM-derived measures are thought to depend on the number of data points analyzed, the minimum number needed to reasonably approximate true values of these measures is unknown. For each of two performance variables related to mechanical stability of gait, we evaluated changes in UCM-derived measures when increasing the number of analyzed points, here steps. Fourteen older adults walked on a treadmill while motion capture tracked movement. For each subject, n steps (where n = 2–99) were randomly sampled from the first 100, then used to calculate UCM-derived variables. For each subject, variables were expressed as a percent of the subject-specific value with n = 100 and averaged across 50 simulations. For each n, 95% confidence intervals (CIs) were calculated from group data. The minimum number of steps to “reasonably approximate” a variables was defined as the value of n for which the lower CI was >90% of the value with n = 100. Regardless of performance variable, reasonable approximations of the synergy index were attained with n = 16 steps, whereas n = 50 steps were needed for each of the variance components However, the differences between using 16 steps and 50 steps were small. Collecting 15–20 steps is recommended for a reasonable approximation of the synergy indices considered herein, particularly when data collection is constrained to a limited number of steps.