Clustering of Directions Improves Goodness of Fit in Kinematic Data Collected in the Transverse Plane During Robot-Assisted Rehabilitation of Stroke Patients

The kinematic character of hand trajectory in reaching tasks varies by movement direction. Often, direction is not included as a factor in the analysis of data collected during multi-directional reach tasks; consequently, this directionally insensitive model (DI) may be prone to type-II error due to unexplained variance. On the other hand, directionally specific models (DS) that account separately for each movement direction, may reduce statistical power by increasing the amount of data groupings. We propose a clustered-by-similarity (CS) in which movement directions with similar kinematic features are grouped together, maximizing model fit by decreasing unexplained variance while also decreasing uninformative sub-groupings. We tested model quality in measuring change over time in 10 kinematic features extracted from 72 chronic stroke patients participating in the VA-ROBOTICS trial, performing a targeted reaching task over 16 movement directions (8 targets, back- and forth from center) in the horizontal plane. Across 49 participants surviving a quality control sieve, 4.3 ± 1.1 (min: 3; max: 7) clusters were found among the 16 movement directions; clusters varied between participants. Among 49 participants, and averaged across 10 features, the better-fitting model for predicting change in features was found to be CS assessed by the Akaike Information criterion (61.6 ± 7.3%), versus DS (31.0 ± 7.8%) and DI (7.1 ± 7.1%). Confirmatory analysis via Extra Sum of Squares F-test showed the DS and CS models out-performed the DI model in head-to-head (pairwise) comparison in >85% of all specimens. Thus, we find overwhelming evidence that it is necessary to adjust for direction in the models of multi-directional movements, and that clustering kinematic data by feature similarly may yield the optimal configuration for this co-variate