The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback–Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

1.
Andrzejewska
,
M.
,
Żebrowski
,
J. J.
,
Rams
,
K.
,
Ozimek
,
M.
, and
Baranowski
,
R.
, “
Assessment of time irreversibility in a time series using visibility graphs
,”
Front. Netw. Physiol.
2
,
877474
(
2022
).
2.
Aoyagi
,
N.
, “
Changes in the Hurst exponent of heart rate variability during physical activity
,”
AIP Conf. Proc.
780
,
599
602
(
2005
).
3.
Azami
,
H.
,
Li
,
P.
,
Arnold
,
S. E.
,
Escudero
,
J.
, and
Humeau-Heurtier
,
A.
, “
Fuzzy entropy metrics for the analysis of biomedical signals: Assessment and comparison
,”
IEEE Access
7
,
104833
104847
(
2019
).
4.
Balagué
,
N.
,
Hristovski
,
R.
,
Almarcha
,
M.
,
Garcia-Retortillo
,
S.
, and
Ivanov
,
P. Ch.
, “
Network physiology of exercise: Vision and perspectives
,”
Front. Physiol.
11
,
611550
(
2020
).
5.
Balagué
,
N.
,
Hristovski
,
R.
,
Almarcha
,
M.
,
Garcia-Retortillo
,
S.
, and
Ivanov
,
P. Ch.
, “
Network physiology of exercise: Beyond molecular and omics perspectives
,”
Sports Med. Open
8
(
1
),
119
(
2022
).
6.
Bandara
,
K. M. E. L. N.
and
Wijesiriwardana
,
R.
, “
Sample entropy analysis of cardiac and respiratory responses during four limbs exercise
,” in
2021 3rd International Conference on Electrical Engineering (EECon)
(Institute of Electrical and Electronics Engineers,
2021
), pp.
106
111
.
7.
Bartsch
,
R. P.
,
Schumann
,
A. Y.
,
Kantelhardt
,
J. W.
,
Penzel
,
T.
, and
Ivanov
,
P. Ch.
, “
Phase transitions in physiologic coupling
,”
Proc. Natl. Acad. Sci. U.S.A.
109
(
26
),
10181
10186
(
2012
).
8.
Bashan
,
A.
,
Bartsch
,
R. P.
,
Kantelhardt
,
J. W.
,
Havlin
,
S.
, and
Ivanov
,
P. C.
, “
Network physiology reveals relations between network topology and physiological function
,”
Nat. Commun.
3
,
702
(
2012
).
9.
Baumert
,
M.
,
Czippelova
,
B.
,
Ganesan
,
A.
,
Schmidt
,
M.
,
Zaunseder
,
S.
, and
Javorka
,
M.
, “
Entropy analysis of RR and QT interval variability during orthostatic and mental stress in healthy subjects
,”
Entropy
16
(
12
),
6384
6393
(
2014
).
10.
Bhaduri
,
A.
and
Ghosh
,
D.
, “
Quantitative assessment of heart rate dynamics during meditation: An ECG based study with multi-fractality and visibility graph
,”
Front. Physiol.
7
,
44
(
2016
).
11.
Bollt
,
E. M.
,
Skufca
,
J. D.
, and
McGregor
,
S. J.
, “
Control entropy: A complexity measure for nonstationary signals
,”
Math. Biosci. Eng.
6
(
1
),
1
25
(
2009
).
12.
Borik
,
S.
,
Keller
,
M.
,
Perlitz
,
V.
,
Lyra
,
S.
,
Pelz
,
H.
,
Müller
,
G.
,
Leonhardt
,
S.
, and
Blazek
,
V.
, “
On the cardiorespiratory coordination assessed by the photoplethysmography imaging technique
,”
Sci. Rep.
13
(
1
),
14645
(
2023
).
13.
Borowska
,
M.
, “
Entropy-Based algorithms in the analysis of biomedical signals
,”
Stud. Logic Grammar Rhetoric
43
(
1
),
21
32
(
2015
).
14.
Cai
,
Z.
,
Cheng
,
H.
,
Xing
,
Y.
,
Chen
,
F.
,
Zhang
,
Y.
, and
Cui
,
C.
, “
Autonomic nervous activity analysis based on visibility graph complex networks and skin sympathetic nerve activity
,”
Front. Physiol.
13
,
1001415
(
2022
).
15.
Costa
,
M.
,
Goldberger
,
A. L.
, and
Peng
,
C. K.
, “
Broken asymmetry of the human heartbeat: Loss of time irreversibility in aging and disease
,”
Phys. Rev. Lett.
95
(
19
),
2
5
(
2005
).
16.
Eduardo Virgilio Silva
,
L.
, and
Otavio Murta
,
L.
, “
Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis
,”
Chaos
22
(
4
),
043105
(
2012
).
17.
Faes
,
L.
and
Porta
,
A.
, “
Conditional entropy-based evaluation of information dynamics in physiological systems
,” in
Directed information measures in neuroscience
(
Springer
,
Berlin
,
2014
), pp.
61
86
.
18.
Fazan
,
F.
,
Brognara
,
F.
,
Fazan Junior
,
R.
,
Murta Junior
,
L.
, and
Virgilio Silva
,
L.
, “
Changes in the complexity of heart rate variability with exercise training measured by multiscale entropy-based measurements
,”
Entropy
20
(
1
),
47
(
2018
).
19.
Flanagan
,
R.
and
Lacasa
,
L.
, “
Irreversibility of financial time series: A graph-theoretical approach
,”
Phys. Lett. A
380
(
20
),
1689
1697
(
2016
).
20.
Flood
,
M. W.
and
Grimm
,
B.
, “
Entropyhub: An open-source toolkit for entropic time series analysis
,”
PLoS ONE
16
(
11
),
e0259448
(
2021
).
21.
Gao
,
J.
,
Hu
,
J.
, and
Tung
,
W.
, “
Entropy measures for biological signal analyses
,”
Nonlinear Dyn.
68
(
3
),
431
444
(
2012
).
22.
Goldberger
,
A. L.
,
Amaral
,
L. A. N.
,
Hausdorff
,
J. M.
,
Ivanov
,
P. Ch.
,
Peng
,
C.-K.
, and
Stanley
,
H. E.
, “
Fractal dynamics in physiology: Alterations with disease and aging
,”
Proc. Natl. Acad. Sci. U.S.A.
99
(
suppl_1
),
2466
2472
(
2002a
).
23.
Goldberger
,
A. L.
,
Peng
,
C. K.
, and
Lipsitz
,
L. A.
, “
What is physiologic complexity and how does it change with aging and disease?
,”
Neurobiol. Aging
23
(
1
),
23
26
(
2002b
).
24.
Gronwald
,
T.
,
Hoos
,
O.
,
Ludyga
,
S.
, and
Hottenrott
,
K.
, “
Non-linear dynamics of heart rate variability during incremental cycling exercise
,”
Res. Sports Med.
27
(
1
),
88
98
(
2019
).
25.
Hausdorff
,
J. M.
, and
Peng
,
C.-K.
, “
Multiscaled randomness: A possible source of 1/f noise in biology
,”
Phys. Rev. E
54
(
2
),
2154
2157
(
1996
).
26.
Henriques
,
T.
,
Ribeiro
,
M.
,
Teixeira
,
A.
,
Castro
,
L.
,
Antunes
,
L.
, and
Costa-Santos
,
C.
, “
Nonlinear methods most applied to heart-rate time series: A review
,”
Entropy
22
(
3
),
309
(
2020
).
27.
Ivanov
,
P. Ch.
, “
The New field of network physiology: Building the human physiolome
,”
Front. Netw. Physiol.
1
,
711778
(
2021
).
28.
Ivanov
,
P. C. H.
,
Liu
,
K. K. L.
, and
Bartsch
,
R. P.
, “
Focus on the emerging new fields of network physiology and network medicine
,”
New J. Phys.
18
(
10
),
100201
(
2016
).
29.
Karavirta
,
L.
,
Costa
,
M. D.
,
Goldberger
,
A. L.
,
Tulppo
,
M. P.
,
Laaksonen
,
D. E.
,
Nyman
,
K.
,
Keskitalo
,
M.
,
Häkkinen
,
A.
, and
Häkkinen
,
K.
, “
Heart rate dynamics after combined strength and endurance training in middle-aged women: Heterogeneity of responses
,”
PLoS ONE
8
,
8
(
2013
).
30.
Lacasa
,
L.
, and
Flanagan
,
R.
, “
Time reversibility from visibility graphs of nonstationary processes
,”
Phys. Rev. E
92
(
2
),
1
13
(
2015
).
31.
Lacasa
,
L.
,
Luque
,
B.
,
Ballesteros
,
F.
,
Luque
,
J.
, and
Nuño
,
J. C.
, “
From time series to complex networks: the visibility graph
,”
Proc. Natl. Acad. Sci.
105
,
4972
(
2008
). .
32.
Lacasa
,
L.
,
Mariño
,
I. P.
,
Miguez
,
J.
,
Nicosia
,
V.
, and
Gómez-Gardeñes
,
J.
, Identifying the hidden multiplex architecture of complex systems
2
,
1
8
(
2017
), See http://arxiv.org/abs/1705.04661.
33.
Lacasa
,
L.
,
Nicosia
,
V.
, and
Latora
,
V.
, “
Network structure of multivariate time series
,”
Sci. Rep.
5
,
1
9
(
2015
).
34.
Lacasa
,
L.
,
Nuñez
,
A.
,
Roldán
,
E.
,
Parrondo
,
J. M. R.
, and
Luque
,
B.
, “
Time series irreversibility: A visibility graph approach
,”
Eur. Phys. J. B
85
,
6
(
2012
).
35.
Ladyman
,
J.
,
Lambert
,
J.
, and
Wiesner
,
K.
, “
What is a complex system?
,”
Eur. J. Philos. Sci.
3
(
1
),
33
67
(
2013
).
36.
Lake
,
D. E.
,
Richman
,
J. S.
,
Griffin
,
M. P.
, and
Moorman
,
J. R.
, “
Sample entropy analysis of neonatal heart rate variability
,”
Am. J. Physiol. Regul. Integr. Compar. Physiol.
283
(
3
),
R789
97
(
2002
).
37.
Leon
,
C.
,
Carrault
,
G.
,
Pladys
,
P.
, and
Beuchee
,
A
., “
Early detection of late onset sepsis in premature infants using visibility graph analysis of heart rate variability
,”
IEEE J. Biomed. Health Inf.
25
(
4
),
1006
1017
(
2021
).
38.
Lewis
,
M. J.
and
Short
,
A. L.
, “
Sample entropy of electrocardiographic RR and QT time-series data during rest and exercise
,”
Physiol. Meas.
28
(
6
),
731
744
(
2007
).
39.
Lipponen
,
J. A.
and
Tarvainen
,
M. P.
, “
A robust algorithm for heart rate variability time series artefact correction using novel beat classification
,”
J. Med. Eng. Technol.
43
(
3
),
173
181
(
2019
).
40.
Lizier
,
J. T.
,
The Local Information Dynamics of Distributed Computation in Complex Systems: Vol. Springer Theses (Illustrated)
(
Springer
,
Berlin
,
2012
).
41.
Makowski
,
D.
,
Pham
,
T.
,
Lau
,
Z. J.
,
Brammer
,
J. C.
,
Lespinasse
,
F.
,
Pham
,
H.
,
Schölzel
,
C.
, and
Chen
,
S. H. A
., “
Neurokit2: A python toolbox for neurophysiological signal processing
,”
Behav. Res. Methods
53
(
4
),
1689
1696
(
2021
).
42.
Makowski
,
D.
et al (
2023
). See https://Neuropsychology.Github.Io/NeuroKit/_modules/Neurokit2/Ecg/Ecg_quality.Html#ecg_quality for “Source Code for neurokit2.ecg.ecg_quality.”
43.
Martinez
,
J. P.
,
Almeida
,
R.
,
Olmos
,
S.
,
Rocha
,
A. P.
, and
Laguna
,
P
., “
A wavelet-based ECG delineator: Evaluation on standard databases
,”
IEEE Trans. Biomed. Eng.
51
(
4
),
570
581
(
2004
).
44.
Martinmäki
,
K.
,
Häkkinen
,
K.
,
Mikkola
,
J.
, and
Rusko
,
H
., “
Effect of low-dose endurance training on heart rate variability at rest and during an incremental maximal exercise test
,”
Eur. J. Appl. Physiol.
104
(
3
),
541
548
(
2008
).
45.
Mateo-March
,
M.
,
Moya-Ramón
,
M.
,
Javaloyes
,
A.
,
Sánchez-Muñoz
,
C.
, and
Clemente-Suárez
,
V. J
., “
Validity of detrended fluctuation analysis of heart rate variability to determine intensity thresholds in elite cyclists
,”
Eur. J. Sport Sci.
23
(
4
),
580
587
(
2023
).
46.
Millar
,
P. J.
,
Rakobowchuk
,
M.
,
Adams
,
M. M.
,
Hicks
,
A. L.
,
McCartney
,
N.
, and
MacDonald
,
M. J.
, “
Effects of short-term training on heart rate dynamics in individuals with spinal cord injury
,”
Auton. Neurosci.
150
(
1–2
),
116
121
(
2009
).
47.
Mrowka
,
R.
,
Cimponeriu
,
L.
,
Patzak
,
A.
, and
Rosenblum
,
M. G.
, “
Directionality of coupling of physiological subsystems: Age-related changes of cardiorespiratory interaction during different sleep stages in babies
,”
Am. J. Physiol.
285
(
6
),
R1395
R1401
(
2003
).
48.
Müller
,
A.
,
Kraemer
,
J. F.
,
Penzel
,
T.
,
Bonnemeier
,
H.
,
Kurths
,
J.
, and
Wessel
,
N.
, “
Causality in physiological signals
,”
Physiol. Meas.
37
(
5
),
R46
R72
(
2016
).
49.
Mushtaq
,
R.
(
2011
). See http://ssrn.com/abstract=1911068Electroniccopyavailableat:https://ssrn.com/abstract=1911068 for “Testing Time Series Data for Stationarity.”
50.
Nielsen
,
F
., “
On a generalization of the Jensen-Shannon divergence and the Jensen-Shannon centroid
,”
Entropy
22
,
2
(
2020
).
51.
Pincus
,
S. M.
, “
Approximate entropy as a measure of system complexity
,”
Proc. Natl. Acad. Sci. U. S. A.
88
(
6
),
2297
2301
(
1991
).
52.
Pincus
,
S. M.
, “
Approximate entropy (ApEn) as a complexity measure
,”
Chaose
5
(
1
),
110
117
(
1995
).
53.
Porta
,
A.
,
Bari
,
V.
,
De Maria
,
B.
, and
Baumert
,
M.
, “
A network physiology approach to the assessment of the link between sinoatrial and ventricular cardiac controls
,”
Physiol. Meas.
38
(
7
),
1472
1489
(
2017
).
54.
Rector
,
J. L.
,
Gijzel
,
S. M. W.
,
van de Leemput
,
I. A.
,
van Meulen
,
F. B.
,
Olde Rikkert
,
M. G. M.
, and
Melis
,
R. J. F.
, “
Dynamical indicators of resilience from physiological time series in geriatric inpatients: Lessons learned
,”
Exp. Gerontol.
149
,
111341
(
2021
).
55.
Richman
,
J. S.
and
Randall Moorman
,
J.
, “
Physiological time-series analysis using approximate entropy and sample entropy
,”
Am. J. Physiol. Heart Circ. Physiol.
278
(
6
),
H2039
H2049
(
2000
).
56.
Rodrigues
,
M. R. D.
,
Draper
,
S. C.
,
Bajwa
,
W. U.
, and
Eldar
,
Y. C.
, “
Introduction to information theory and data science
,” in
Information-Theoretic Methods in Data Science
(
Cambridge University Press
,
2021
), pp.
1
43
.
57.
Rogers
,
B.
,
Giles
,
D.
,
Draper
,
N.
,
Hoos
,
O.
, and
Gronwald
,
T.
, “
A New detection method defining the aerobic threshold for endurance exercise and training prescription based on fractal correlation properties of heart rate variability
,”
Front. Physiol.
11
,
596567
(
2021
).
58.
Rogers
,
B.
and
Gronwald
,
T.
, “
Fractal correlation properties of heart rate variability as a biomarker for intensity distribution and training prescription in endurance exercise: An update
,”
Front. Physiol.
13
,
879071
(
2022
).
59.
Rojo-Alvarez
,
J. L.
,
Sanchez-Sanchez
,
A.
,
Barquero-Perez
,
O.
,
Goya-Esteban
,
R.
,
Everss
,
E.
,
Mora-Jimenez
,
I.
, and
Garcia-Alberola
,
A.
, “
Analysis of physiological meaning of detrended fluctuation analysis in heart rate variability using a lumped parameter model
,” in
2007 Computers in Cardiology
(Institute of Electrical and Electronics Engineers,
2007
), pp.
25
28
.
60.
Roldán
,
É.
and
Parrondo
,
J. M. R.
, “
Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
,”
Phys. Rev. E
85
(
3
) (
2012
).
61.
Schelter
,
B.
,
Dahlhaus
,
R.
,
Leistritz
,
L.
,
Hesse
,
W.
,
Schack
,
B.
,
Kurths
,
J.
,
Timmer
,
J.
, and
Witte
,
H.
, “
Multivariate time series analysis
,”
Mathematical Methods in Signal Processing and Digital Image Analysis
(
Springer
,
Berlin
,
2008
), pp.
1
40
.
62.
Seely
,
A. J. E.
and
Macklem
,
P.
, “
Fractal variability: An emergent property of complex dissipative systems
,”
Chaos
22
,
1
(
2012
).
63.
Silva
,
L. E. V.
,
Cabella
,
B. C. T.
,
Neves
,
U. P. D. C.
, and
Murta Junior
,
L. O.
, “
Multiscale entropy-based methods for heart rate variability complexity analysis
,”
Physica A
422
,
143
152
(
2015
).
64.
Solís-Montufar
,
E. E.
,
Gálvez-Coyt
,
G.
, and
Muñoz-Diosdado
,
A.
, “
Entropy analysis of RR-time series from stress tests
,”
Front. Physiol.
11
,
981
(
2020
).
65.
Tonhajzerova
,
I.
,
Ondrejka
,
I.
,
Chladekova
,
L.
,
Farsky
,
I.
,
Visnovcova
,
Z.
,
Calkovska
,
A.
,
Jurko
,
A.
, and
Javorka
,
M.
, “
Heart rate time irreversibility is impaired in adolescent major depression
,”
Prog. Neuro-Psychopharmacol. Biol. Psychiatry
39
(
1
),
212
217
(
2012
).
66.
Valente
,
M.
,
Javorka
,
M.
,
Porta
,
A.
,
Bari
,
V.
,
Krohova
,
J.
,
Czippelova
,
B.
,
Turianikova
,
Z.
,
Nollo
,
G.
, and
Faes
,
L.
, “
Univariate and multivariate conditional entropy measures for the characterization of short-term cardiovascular complexity under physiological stress
,”
Physiol. Meas.
39
(
1
),
014002
(
2018
).
67.
Xiong
,
W.
,
Faes
,
L.
, and
Ivanov
,
P. C.
, “
Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations
,”
Phys. Rev. E
95
(
6
),
1
37
(
2017
).
68.
Yentes
,
J. M.
,
Hunt
,
N.
,
Schmid
,
K. K.
,
Kaipust
,
J. P.
,
McGrath
,
D.
, and
Stergiou
,
N.
, “
The appropriate use of approximate entropy and sample entropy with short data sets
,”
Ann. Biomed. Eng.
41
(
2
),
349
365
(
2013
).

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