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

Mohamed Refai, Mohamed Irfan; Saes, Mique; Scheltinga, Bouke L.; van Kordelaar, Joost; Bussmann, Johannes B. J.; Veltink, Peter H.; Buurke, Jaap H.; Meskers, Carel G. M.; van Wegen, Erwin E. H.; Kwakkel, Gert; van Beijnum, Bert-Jan F.

doi:10.1186/s12984-021-00949-6

Journal of NeuroEngineering and Rehabilitation

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)
Metric (Feasible Range)	Base Velocity Profile	Min	Max	%Δ (%)	Min	Max	CE (%)	Min	Max	SNR (dB)	Min	Max	SNR (dB)	Min	Max
NOS* (1–7)	v_symm	1	2	50	1	7	10.7	1	7	N.A	1	7	N.A	1	3
NOS* (1–7)	v_asymm	3	7	N.A	3	7	1.2	4	7	N.A	4	7	N.A	3	7
SM (0–1)	v_symm	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
SM (0–1)	v_asymm	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)	v_symm	0.8	0.8	0	0.8	1	3.2	0.8	0.9	–	0.8	0.9	–	0.7	0.9
MAPR (0–1)	v_asymm	0.8	0.8	0	0.7	0.9	0.6	0.7	0.9	–	0.7	0.9	–	0.7	0.9
VAL* (− ∞–∞)	v_symm	− 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
VAL* (− ∞–∞)	v_asymm	− 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–∞)	v_symm	1	1	0	1	25	92.2	1	36	45	1	16	43.3	1	3
Peaks* (1–∞)	v_asymm	1	1	0	1	25	93.4	1	35	45.4	1	16	43.7	1	2
IPV (− ∞–1)	v_symm	1	1	0	0	1	92.2	0	1	45	0	1	43.3	0.2	1
IPV (− ∞–1)	v_asymm	1	1	0	0	1	93.4	0	1	45.4	0	1	43.7	0.3	1
DSJt* (0–∞)	v_symm	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
DSJt* (0–∞)	v_asymm	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–∞)	v_symm	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
LDSJt* (0–∞)	v_asymm	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–∞)	v_symm	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
DSJb* (0–∞)	v_asymm	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–∞)	v_symm	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
LDSJb* (0–∞)	v_asymm	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)	v_symm	1	1	0	0.8	1	34.5	0.9	1	–	1	1	–	− 0.2	1
CM (− 1–1)	v_asymm	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)	v_symm	0.1	1	774.4	0.1	0.2	93.5	0	0.2	39	0	0.2	35.3	0.2	0.5
SPMR (0–1)	v_asymm	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–∞)	v_symm	− 1	− 1	0	− 1.4	− 1	57	− 2.1	− 1	27	− 1.6	− 1	25.8	− 1.8	− 1
SPM (0–∞)	v_asymm	− 1	− 1	0	− 1.4	− 1	55	− 2.1	− 1	27.4	− 1.6	− 1	26.8	− 2	− 1
SPAL (0–∞)	v_symm	− 2.1	− 1.9	11	− 3	− 2	50	− 2.3	− 2	–	− 2.3	− 2	–	− 3.4	− 1.9
SPAL (0–∞)	v_asymm	− 2	− 1.8	12.2	− 3	− 1.8	54.7	− 2.2	− 1.9	–	− 2.2	− 1.8	–	− 3.8	− 1.9
SPARC (0–∞)	v_symm	− 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
SPARC (0–∞)	v_asymm	− 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

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)

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ISSN: 1743-0003

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