Phase plane quantification of single-joint smoothness

Abstract

We report a metric of single joint movement smoothness based on phase plane analysis of trajectories of the wrist about the elbow. Overall smoothness was quantified as the Phase Area Ratio (PAR), comparing the total area circumscribed by the acceleration-velocity (A-V) curve, to the area of its convex hull; PAR ranges from 0 (perfectly smooth) to 1 (gross motor impairment). Elbow flexion records obtained from a cohort study showed that PAR was significantly different in intact (PAR = 9.4x10^-4 ± 6.6x10^-4, group average, N = 18) versus chronic stroke patients (0.11 ± 0.15, N = 9; Wilcoxon rank-sum on group means: P < .0001).  Separate simulations showed that PAR was appropriately insensitive to velocity asymmetry and to scale factors, e.g. range of motion, peak- and average velocity, and movement duration. We conclude that PAR is an attractive smoothness measure, as it accomplishes four objectives: 1) insensitivity to scale factors unrelated to trajectory shape, 2) discrimination of an intact versus impaired cohort, 3) reporting a near-zero impairment for healthy actors, responding appropriately to asymmetries commonly observed in human movement, and 4) operation on a fixed, closed scale.