Quantifying neurophysiological mechanism through heart rate variability: the case of cognitive stress

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The metrics considered in the non-linear domain and their values under stress and rest conditions

Metric	References	Meta analysis report		Stress		Rest
		Weight	Characteristics	Mean	Stdd	Mean	Stdd
D1(-)	Vuksanović (2007)	0.5049	Very high	1	0.17	0.90	0.18
	Melillo et al. (2011)	0.4942	Very low	1.04	0.45	1.43	0.17
D2(-)	Schubert et al. (2009)	0.5413	Very low	3.3	0.34	3.42	0.29
	Melillo et al. (2013)	0.4590	Very low	1.62	1.30	2.92	1.07
	Melillo et al. (2011)	-	Low	0.74	0.12	0.76	0.19
En(0.2) (–)	Melillo et al. (2011)	-	Very low	1	0.30	1.10	0.14
En(rchon) (–)	Melillo et al. (2011)	-	Very low	1	0.25	1.17	0.12
En(rmax) (–)	Melillo et al. (2013)	-	Low	1.06	0.18	1.15	0.14
LLE	Vuksanović (2007)	-	High	0.05	0.018	0.05	0.017
Lmax (beats)	Melillo et al. (2011)	-	Very low	213.30	137.12	285.90	111.32
Lmean (beats)	Melillo et al. (2011)	-	Very high	14.90	6.82	11.07	2.47
RECdet (%)	Melillo et al. (2011)	-	High	98.57	1.30	98.70	0.87
RECrate (%)	Melillo et al. (2011)	-	Very high	42.30	12.80	33.49	6.30
SampEn (–)	Vuksanović (2007)	-	Very low	1.72	0.05	1.80	0.03
SD1 (ms)	Melillo et al. (2011)	-	Very low	0.03	0.02	0.04	0.02
SD2 (ms)	Melillo et al. (2011)	-	Very low	0.06	0.02	0.09	0.04
ShnEn (–)	Melillo et al. (2011)	-	Very high	3.46	0.40	3.18	0.24

The metrics considered in the time domain and their values under stress and rest conditions

Metric	References	Meta analysis report		Stress		Rest
		Mean %-tile	Characteristics	Mean	Stdd	Mean	Stdd
MeanRR	Vuksanović (2007)	0.0033	Low	740.74	263.25	806.59	249.54
	Tharion et al. (2009)	0.0117	Very low	777.49	114.38	867.36	114.12
	Schubert et al. (2009)	0.0183	Low	686.47	240.82	808.67	206.25
	Papousek et al. (2010)	0.0926	Very low	617.92	210.44	819.73	244.14
	Lackner et al. (2011)	0.1287	Low	765.93	314.33	837.15	324.60
	Taelman et al. (2011)	0.1997	Very low	755.44	134.52	863.54	147.12
RRStdd	Tharion et al. (2009)	0.0894	Very low	52.42	21.51	74.32	25.21
	Schubert et al. (2009)	0.0352	Very high	96.25	86.38	33.54	23.44
	Taelman et al. (2011)	0.0376	Very low	35.27	16.22	46.38	19.49
	Visnovcova et al. (2014)	0.5005	Very low	48.22	17.74	56.53	21.71
RRMmsds	Li et al. (2009)	0.2685	Very low	55.44	29.22	68.51	37.42
	Tharion et al. (2009)	0.0417	Low	49.92	31.07	74.03	39.65
	Taelman et al. (2011)	0.5438	Very low	19.42	13.04	28.47	16.04
NN50p (%)	Tharion et al. (2009)	0.2152	Very low	20.21	19.07	39.03	23.02
	Taelman et al. (2011)	0.7842	Low	26.52	16.67	31.42	18.37
	Sieciński (2019)	0.3229	Low	15.36	14.42	37.06	21.54

The metrics considered in the frequency domain and their values under stress and rest conditions

Metric	References	Meta analysis report		Stress		Rest
		Mean %-tile	Characteristics	Mean	Stdd	Mean	Stdd
LowF (ms2)	Hjortskov et al. (2004)	8.52	Very low	1400	1030	1664	807.88
	Vuksanović (2007)	15.68	Very high	608	458.12	454.90	382
	Tharion et al. (2009)	5.75	Very low	1193	724.15	2155	2156
	Papousek et al. (2010)	14.25	High	1645	986.91	997.30	600.10
	Lackner et al. (2011)	10.16	High	1342	1205	813.17	650
	Traina et al. (2011)	15.32	Very high	1245	312	512	115
	Taelman et al. (2011)	14.82	Very low	468.10	460.20	869.53	641
HighF (ms2)	Hjortskov et al. (2004)	5.42	Very low	1312	715	1775	1093
	Vuksanović (2007)	11.44	Very low	445	1081	638.90	1340
	Vuksanović (2007)	9.67	High	664.92	924.88	556.10	715
	Tharion et al. (2009)	1.52	Very low	1695	2093	2891	2623
	Li et al. (2009)	8.36	Very low	1202	1455	2002	2065
	Li et al. (2009)	11.80	Very low	1072	1056	1675	1752
	Papousek et al. (2010)	18.13	Low	667	402	1098	663
	Traina et al. (2011)	17.88	Low	253.15	264.20	277.60	245
	Taelman et al. (2011)	15.63	Very low	552	421	1001	785
	Sieciński (2019)	15.07	High	1157.22	2545.10	889.20	1526.24
HighF/LowF	Hjortskov et al. (2004)	14.92	High	2.12	1.08	1.15	0.75
	Kofman et al. (2006)	20.19	High	1.61	1.02	1.12	0.68
	Vuksanović (2007)	4.67	Low	1.06	4.12	1.08	3.11
	Tharion et al. (2009)	12.76	High	1.32	0.78	1.40	1.78
	Schubert et al. (2009)	19.85	High	1.23	1.20	1.48	1.11
	Papousek et al. (2010)	23.10	High	1.14	0.63	0.01	0.76
	Traina et al. (2011)	4.65	Very high	6.12	2.88	3.10	2.10
	Sieciński (2019)	10.14	Very low	0.999	0.14	0.0005	0.0014

Different measures and definitions of the recurrence plot

Measure	Definition
Recurrence rate/recurrence points percentage in an RP corresponding to the correlation sum	RR=1M2∑i,j=1MRi,j RR = {1 \over {{M^2}}}\sum\limits_{i,j = 1}^M {{R_{i,j}}}
Recurrence points percentage forming diagonal lines	RECdet=∑q=qminMqPq/∑q=1MqPq RE{C_{det}} = \mathop \sum \nolimits_{q = {q_{min }}}^M qP\left( q \right)/\mathop \sum \nolimits_{q = 1}^M qP\left( q \right)
Uncountable/the percentage of recurrence points which form vertical lines	RECl=∑s=sminMsPs/∑s=1MsPs RE{C_l} = \mathop \sum \nolimits_{s = {s_{min }}}^M sP\left( s \right)/\mathop \sum \nolimits_{s = 1}^M sP\left( s \right)
The proportion among DET and RR	RECrate=M2∑q=qminMqPq/∑q=1MqPq2 RE{C_{rate}} = {M^2}\mathop \sum \nolimits_{q = {q_{min }}}^M qP\left( q \right)/{\left( {\mathop \sum \nolimits_{q = 1}^M qP\left( q \right)} \right)^2}
Average length of the diagonal lines	Qavg=∑q=qminMqPq/∑q=1MPq {Q_{avg}} = \mathop \sum \nolimits_{q = {q_{min }}}^M qP\left( q \right)/\mathop \sum \nolimits_{q = 1}^M P\left( q \right)
Average length of the vertical lines/trapping time	TT=∑s=sminMsPs/∑s=sminMPs TT = \mathop \sum \nolimits_{s = {s_{min }}}^M sP\left( s \right)/\mathop \sum \nolimits_{s = {s_{min }}}^M P\left( s \right)
Length of the longest diagonal line	Qm=maxqi;i=1,⋯,⋯Nq {Q_m} = {{max}}\left( {\left\{ {{q_i};i = 1, \cdots , \cdots {N_q}} \right\}} \right)
Length of the longest vertical line	Sm=maxsi;i=1,⋯,⋯Ns {S_m} = {{max}}\left( {\left\{ {{s_i};i = 1, \cdots , \cdots {N_s}} \right\}} \right)
Divergence, related with the KS entropy of the system, i.e., with the sum of the positive Lyapunov exponents	DIV=1/Qmax DIV = 1/{Q_{max }}
ShnEn of the probability distribution of the diagonal line lengths p(q)	En=−∑q=qminMPqlnPq {E_n} = - \mathop \sum \nolimits_{q = {q_{min }}}^M P\left( q \right)ln\left( {P\left( q \right)} \right)
The paling of the RR towards its edges	RRtrend=∑i=1Ui−U2RRi−RRi/∑i=1Ui−U22 {RR_{trend}} = \mathop \sum \nolimits_{i = 1}^U \left( {i - {U \over 2}} \right)\left( {{RR_i} - {RR_i}} \right)/\mathop \sum \nolimits_{i = 1}^U {\left( {i - {U \over 2}} \right)^2}