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Table 2 Simulation Analysis for each metric and its changes

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

Metric (Feasible Range) Base Velocity Profile Shape Sinus Noise Filtered noise Sub-movements (N = 2)
Min Max %Δ (%) Min Max CE (%) Min Max SNR (dB) Min Max SNR (dB) Min Max
NOS*
(1–7)
vsymm 1 2 50 1 7 10.7 1 7 N.A 1 7 N.A 1 3
vasymm 3 7 N.A 3 7 1.2 4 7 N.A 4 7 N.A 3 7
SM
(0–1)
vsymm 0.5 0.5 0 0.4 0.6 63.6 0.4 0.5 18.6 0.4 0.6 0.5 0.7
vasymm 0. 5 0.5 0 0.4 0.5 56 0.3 0.5 18.6 0.4 0.5 0.4 0.5
MAPR
(0–1)
vsymm 0.8 0.8 0 0.8 1 3.2 0.8 0.9 0.8 0.9 0.7 0.9
vasymm 0.8 0.8 0 0.7 0.9 0.6 0.7 0.9 0.7 0.9 0.7 0.9
VAL*
(− ∞–∞)
vsymm − 2E − 04 − 1.6E − 05 91.7 − 1E− 03 − 5.7E − 04 21.6 − 9.7E − 03 5.6E − 03 25 − 9.7E − 03 − 7.2E − 03 19 − 4.9E − 03 − 2E − 03
vasymm − 2E − 04 − 1.7E − 05 91.7 − 1E − 03 − 6.6E − 04 16.2 − 9.7E − 03 4.2E − 03 24.6 − 9.7E − 03 − 7.9E − 03 18.2 − 4.9E − 03 − 2E − 03
Peaks*
(1–∞)
vsymm 1 1 0 1 25 92.2 1 36 45 1 16 43.3 1 3
vasymm 1 1 0 1 25 93.4 1 35 45.4 1 16 43.7 1 2
IPV
(− ∞–1)
vsymm 1 1 0 0 1 92.2 0 1 45 0 1 43.3 0.2 1
vasymm 1 1 0 0 1 93.4 0 1 45.4 0 1 43.7 0.3 1
DSJt*
(0–∞)
vsymm 19 19 0 17.4 8.2E + 3 96.3 18.7 5.2E + 03 45 18.5 885.6 49.3 18.8 95.6
vasymm 36.4 36.7 0.1 34.4 8.2E + 3 94 34.4 5.2E + 3 45.4 33.3 889.8 49.7 34.6 179.6
LDSJt*
(0–∞)
vsymm 2.9 2.9 0 2.9 9 95.1 2.9 8.6 45 2.9 6.8 49.3 2.9 4.6
vasymm 3.6 3.6 0 4 9 90.9 3.5 8.6 45.4 3.5 6.8 43.7 3.5 5.2
DSJb*
(0–∞)
vsymm 204.6 204.8 0.1 162.5 2.1E + 07 96.9 194.8 9.9E + 06 45 191.4 3.8E + 05 49.3 199.7 4.3E + 03
vasymm 548 549.3 0.3 489.1 1.6E + 07 95 478.6 8.5E + 06 45.4 457 2.7E + 05 49.7 437 1.1E + 04
LDSJb*
(0–∞)
vsymm 5.3 5.3 0 5.1 16.9 95.1 5.3 16.1 45 5.3 12.9 49.3 5.3 8.4
vasymm 6.3 6.3 0 6.2 16.6 91.6 6.2 16 45.4 6.1 12.5 46.7 6.1 9.3
CM
(− 1–1)
vsymm 1 1 0 0.8 1 34.5 0.9 1 1 1 − 0.2 1
vasymm 0.6 0.6 0.1 0.4 0.6 26.7 0.6 0.7 0.6 0.7 − 0.1 0.8
SPMR
(0–1)
vsymm 0.1 1 774.4 0.1 0.2 93.5 0 0.2 39 0 0.2 35.3 0.2 0.5
vasymm 0.1 0.9 1E + 03 0.1 0.2 76.9 0 0.2 39.4 0 0.2 32.8 0.1 0.3
SPM
(0–∞)
vsymm − 1 − 1 0 − 1.4 − 1 57 − 2.1 − 1 27 − 1.6 − 1 25.8 − 1.8 − 1
vasymm − 1 − 1 0 − 1.4 − 1 55 − 2.1 − 1 27.4 − 1.6 − 1 26.8 − 2 − 1
SPAL
(0–∞)
vsymm − 2.1 − 1.9 11 − 3 − 2 50 − 2.3 − 2 − 2.3 − 2 − 3.4 − 1.9
vasymm − 2 − 1.8 12.2 − 3 − 1.8 54.7 − 2.2 − 1.9 − 2.2 − 1.8 − 3.8 − 1.9
SPARC
(0–∞)
vsymm − 1.4 − 1.4 1 − 2.9 − 1.4 66.9 − 2.2 − 1.4 15.1 − 2.2 − 1.4 19 − 2.7 − 1.4
vasymm − 1.4 − 1.4 0.4 − 2.8 − 1.4 66.3 − 2.1 − 1.4 14.7 − 2.1 − 1.4 18.2 − 3.1 − 1.4
  1. Assessing the response of each metric by comparing the effect of perturbation against the base velocity profile: Δ%: percentage difference in metric value from the base velocity profiles (instances where the metric depends on the shape are in bold), CE(%): percentage of combinations where the metric value differs by at least 10% from base velocity profiles, SNR(dB): the signal-to-noise ratio at which the metric differs by at least 10% from the base profile. Note that a higher added RMS noise value corresponds to a lower SNR value, and hence to a greater robustness to noise. Metrics included are NOS* (number of sub-movements), SM (speed metric), MAPR (movement arrest period ratio), VAL* (velocity arc length), Peaks* (number of peaks), IPV (inverse of number of peaks and valleys), DSJt* and DSJb* (Dimensionless squared jerk), LDSJb* and LDSJt* (log of DSJt* and DSJb*), CM (correlation metric), SPMR (spectral metric), SPM (spectral method), SPAL (spectral arc length 2012), and SPARC (spectral arc length)