Reformulation in the Phase Plane Enhances Smoothness Rater Accuracy in Stroke

A Generalized Strategy for Measuring Performance in the Velocity-Position Phase Plane

“…However, recent evidence suggests that remediation may be possible by reformulating elements of the jerk integral as a function of limb position, not time (Wininger, Kim, & Craelius, 2009;Wininger, Kim, & Craelius, 2012). However, transformation into the phase plane creates complications.…”

“…( 2) where θ i,f are the initial and final angular position,θ (θ ) is angular velocity as a function of joint position, and K is again an arbitrary coefficient, for example, −(max[θ(θ )] · (θ f − θ i )) −1 , which normalizes the phase portrait to unity in the ordinate (angular velocity) and abscissa (angular range), placing the trace on the unit square (Wininger et al, 2012). However, this expression is only valid for 1-D angular data with no movement reversals (i.e., completely monotonic position data.…”

“…By substituting position for time at the earliest possible juncture, it is thought that the essence of ISJ is captured in phase jerk (PJ), equivalent to a rephrasing the jerk integral as a function of position (Wininger et al, 2012):…”

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

“…In addition to basic movement parameters of amplitude, duration, average-and peak velocity, average-and peak acceleration, we calculated four descriptors related to movement smoothness including the number of peaks in the velocity trace (Fetters and Todd, 1987;Michaelsen et al, 2006;Thelen et al, 1993), the tent metric i.e., the ratio of the area under the convex hull fitted to the velocity trace versus the area under the velocity trace itself (Rohrer et al, 2002), and two formulations of jerk (Hogan and Sternad, 2009;Rohrer et al, 2002). Where jerk-based metrics have been shown to be especially sensitive to basic movement parameters (Wininger et al, 2009(Wininger et al, , 2012, we tested one formulation witha widely analyzed behavior…”

“…Because these features are expected to be highly collinear (Wininger et al, 2009(Wininger et al, , 2012, feature set dimensionality was reduced via Principal Components Analysis (PCA) over the entire dataset, i.e., all participants all days. A minimum threshold was established a priori at 80%: the minimum number of PCs accounting for greater than 80% of the variance would be retained for analysis.…”