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Table 1 Overview of Smoothness metrics identified from the literature

From: Smoothness metrics for reaching performance after stroke. Part 1: which one to choose?

Metric (Abbreviation) Units Articles useda Exclusions Category Earliest citation
Index of curvature (IC) [] 1 E3 Trajectory [33]
Standard deviation in 2D plane (SD_XY) [] 1 E3 Trajectory [72]
Number of sub-movements (NOS) [] 1   Velocity [37]
Speed metric (SM) [] 15   Velocity [14]
Normalized reaching speed (NRS) [] 2 E4 (SM) Velocity [35]
Movement arrest period ratio (MAPR) [] 3   Velocity [34]
Tent Metric (TM) [] 1 E2 Velocity [14]
Velocity Arc Length (VAL) [] 1   Velocity [4]
Correlation Metric (CM) [] 2   Velocity [38]
Peaks Metric (Peaks) [] 61   Acceleration [39]
Number of Movement Units (NMU) [] 3 E4a (Peaks) Acceleration [73]
Number of peaks normalized by movement duration (NPt) [s−1] 1 E1 Acceleration [40]
Number of peaks normalized by movement distance (NPd) [m−1] 3 E1 Acceleration [41]
Inverse number of peaks and valleys (IPV) [] 1   Acceleration [44]
Acceleration metric (AM) [] 2 E1 Acceleration [35]
Integrated absolute jerk (IAJ) [ms−2] 2 E1 Jerk [74]
Mean absolute jerk (MAJ) [ms−3] 2 E1 Jerk [33]
Mean absolute jerk normalized by peak speed (MAJPS) [s−2] 7 E1 Jerk [14]
Integrated squared jerk (ISJ) [m2s−5] 1 E1 Jerk [75]
Root mean squared jerk metric (RMSJ) [ms−3] 1 E1 Jerk [76]
Normalized integrated jerk (NIJ) [ms−3 \(\sqrt{\mathrm{s}}\)] 1 E1 Jerk [77]
Dimensionless squared jerk (DSJt) [] 12   Jerk [3]
Log dimensionless squared jerk (LDSJt) [] 1   Jerk [5]
Dimensionless squared jerk (DSJm) [] 1 E4a (DSJt) Jerk [2]
Dimensionless squared jerk (DSJb) [] 1   Jerk [4]
Log dimensionless squared jerk (LDSJb) [] 1   Jerk [4]
Rotational jerk (RJ) [] 1 E3 Jerk [48]
Spectral metric (SPMR) [] 1   Frequency [49]
Spectral method (SPM) [] 1   Frequency [1]
Spectral arc length 2012 (SPAL) [] 8   Frequency [4]
Spectral arc length (SPARC) [] 1   Frequency [6]
Combined smoothness metric (CSM) [− −]b 1 E1 Other [78]
  1. aNumber of articles in the systematic review that used the metric. bUnits were not available. Exclusion criteria include E1: metric was not dimensionless; E2: metric not reproducible from the literature; E3: metric not based on velocity or its derivative; and E4: metric linearly related to another metric (shown in brackets) by (a) scaling or (b) addition of a constant