We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that—in comparison with real data—the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to model heart rate variability in sleep disorders. This possibility is briefly discussed.
References
1.
G.
Parati
, G.
Mancia
, M.
Di Rienzo
, and P.
Castiglioni
, “Point: Counterpoint: Cardiovascular variability is/is not an index of autonomic control of circulation
,” J. Appl. Physiol.
101
, 676
–682
(2006
).2.
L. T.
Mainardi
, “On the quantification of heart rate variability spectral parameters using time-frequency and time-varying methods
,” Philos. Trans. R. Soc. A
367
, 255
–275
(2009
).3.
Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology
, “Heart rate variability. Standards of measurements, physiological interpretation, and clinical use
,” Circulation
93
, 1043
–1065
(1996
).4.
D. T.
Schmitt
, P. K.
Stein
, and P. C.
Ivanov
, “Stratification pattern of static and scale-invariant dynamic measures of heartbeat fluctuations across sleep stages in young and elderly
,” IEEE Trans. Biomed. Eng.
56
, 1564
–1573
(2009
).5.
K. K.
Tripathi
, “Very low frequency oscillations in the power spectra of heart rate variability during dry supine immersion and exposure to non-hypoxic hypobaria
,” Physiol. Meas.
32
, 717
–729
(2011
).6.
J. A.
Taylor
, D. L.
Carr
, C. W.
Myers
, and L.
Eckberg
, “Mechanisms underlying very-low-frequency RR-interval oscillations in humans
,” Circulation
98
, 547
–555
(1998
).7.
L.
Bernardi
, F.
Valle
, M.
Coco
, A.
Calciati
, and P.
Sleight
, “Physical activity influences heart rate variability and very-low-frequency components in Holter electrocardiograms
,” Cardiovasc. Res.
32
, 234
–237
(1996
).8.
M.
Kobayashi
and M.
Toshimitsu
, “1/f fluctuation of heartbeat period
,” IEEE Trans. Biomed. Eng.
BME-29
, 456
–457
(1982
).9.
A. L.
Goldberger
, L. A. N.
Amaral
, J. M.
Hausdorff
, P. Ch.
Ivanov
, C.-K.
Peng
, and H. E.
Stanley
, “Fractal dynamics in physiology: Alterations with disease and aging
,” Proc. Natl. Acad. Sci.
99
, 2466
–2472
(2002
).10.
P. C.
Ivanov
, L. A. N.
Amaral
, A. L.
Goldberger
, S.
Havlin
, M. G.
Rosenblum
, M. G.
Struzik
, and H. E.
Stanley
, “Multifractality in human heartbeat dynamics
,” Nature
399
, 461
–465
(1999
).11.
P. C.
Ivanov
, L. A. N.
Amaral
, A. L.
Goldberger
, S.
Havlin
, M. G.
Rosenblum
, H. E.
Stanley
, and M. G.
Struzik
, “From 1/f noise to multifractal cascades in heartbeat dynamics
,” Chaos
11
, 641
–652
(2001
).12.
D. C.
Lin
, “Simulate heart rate variability in different physiological conditions
,” Comput. Cardiol.
29
, 149
–152
(2002
).13.
J. M.
Karemaker
and J.
Strackee
, “Hemodynamic fluctuations and baroreflex sensitivity in humans: A beat-to-beat model
,” Am. J. Physiol.
253
, 680
–689
(1987
).14.
S. M.
Ryan
, A. L.
Goldberger
, S. M.
Pincus
, J.
Mietus
, and L. A.
Lipsitz
, “Gender-and age-related differences in heart rate dynamics: Are women more complex than men?
,” J. Am. Coll. Cardiol.
24
, 1700
–1707
(1994
).15.
I.
Antelmi
, R. S.
De Paula
, A. R.
Shinzato
, C. A.
Peres
, A. J.
Mansur
, and C. J.
Grupi
, “Influence of age, gender, body mass index, and functional capacity on heart rate variability in a cohort of subjects without heart disease
,” Am. J. Cardiol.
93
, 381
–385
(2004
).16.
P. C.
Ivanov
, M. G.
Rosenblum
, C. K.
Peng
, J.
Mietus
, S.
Havlin
, H.
Stanley
, and A. L.
Goldberger
, “Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis
,” Nature
383
, 323
–327
(1996
).17.
P. C.
Ivanov
, M. G.
Rosenblum
, C. K.
Peng
, J.
Mietus
, S.
Havlin
, H.
Stanley
, and A. L.
Goldberger
, “Scaling and universality in heart rate variability distributions
,” Physica A
249
, 587
–593
(1998
).18.
J. M.
Shneerson
, Sleep Medicine: A Guide to Sleep and its Disorders
(Blackwell Publishing Ltd.
, Oxford
, 2005
).19.
T.
Penzel
, C. C.
Lo
, P. C.
Ivanov
, K.
Kesper
, H. F.
Becker
, and C.
Vogelemeier
, “Analysis of sleep fragmentation and sleep structure in patients with sleep apnea and normal volunteers
,” in Proceedings of the 27th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc.
(IEEE
, Shanghai
, 2005
), pp. 2591
–2594
.20.
E.
Vanoli
, P. B.
Adamson
, G. D.
Pinna
, R.
Lazzara
, and W. C.
Orr
, “Heart rate variability during specific sleep stages a comparison of healthy subjects with patients after myocardial infarction
,” Circulation
91
, 1918
–1922
(1995
).21.
C.
Schäfer
, M. G.
Rosenblum
, J.
Kurths
, and H. H.
Abel
, “Heartbeat synchronized with ventilation
,” Nature
392
, 239
–240
(1998
).22.
M. B.
Lotrič
and A.
Stefanovska
, “Synchronization and modulation in the human cardiorespiratory system
,” Physica A
283
, 451
–461
(2000
).23.
P. C.
Ivanov
, L. N.
Amaral
, A. L.
Goldberger
, and H. E.
Stanley
, “Stochastic feedback and the regulation of biological rhythms
,” Europhys. Lett.
43
, 363
–368
(1998
).24.
J. W.
Kantelhardt
, S.
Havlin
, and P. Ch.
Ivanov
, “Modeling transient correlations in heartbeat dynamics during sleep
,” Europhys. Lett.
62
, 147
–153
(2003
).25.
P. D.
Welch
, “The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
,” IEEE Trans. Audio & Electroacoust
15
, 70
–73
(1967
).26.
A. H.
Khandoker
, C.
Karmakar
, M.
Brennan
, M.
Palaniswami
, and A.
Voss
, Poincaré Plot Methods for Heart Rate Variability Analysis
(Springer
, New York
, 2013
).27.
J.
Gierałtowski
, J. J.
Żebrowski
, and R.
Baranowski
, “Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia
,” Phys. Rev. E
85
, 021915
(2012
).28.
J. W.
Kantelhardt
, S. A.
Zschiegner
, E.
Koscielny-Bunde
, S.
Havlin
, A.
Bunde
, and H. E.
Stanley
, “Multifractal detrended fluctuation analysis of nonstationary time series
,” Physica A
316
, 87
–114
(2002
).29.
W.
Shi
, P.
Shang
, J.
Wang
, and A.
Lin
, “Multiscale multifractal detrended cross-correlation analysis of financial time series
,” Physica A
403
, 35
–44
(2014
).30.
J.
Huang
and P.
Shang
, “Multiscale multifractal diffusion entropy analysis of financial time series
,” Physica A (Oxford)
420
, 221
–228
(2015
).31.
J.
Wang
, P. J.
Shang
, and X. R.
Cui
, “Multiscale multifractal analysis of traffic signals to uncover richer structures
,” Phys. Rev. E
89
, 032916
(2014
).32.
See http://physionet.org/physiotools/mma/ for more information about MMA method and download sample implementation.
33.
A. L.
Goldberger
et al., “Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals
,” Circulation
101
, e215
–e220
(2000
).34.
D.
Kokosińska
and J. J.
Gierałtowski
, “The analysis of human heart rate for healthy and ill patients using the recently published method multiscale multifractal analysis
,” Comput. Cardiol.
41
, 425
–428
(2014
).35.
P. E.
McSharry
, G.
Clifford
, L.
Tarassenko
, and L. A.
Smith
, “Method for generating an artificial RR tachogram of a typical healthy human over 24-h
,” Comput. Cardiol.
29
, 225
–228
(2002
).36.
P. E.
McSharry
and G.
Clifford
, “A statistical model of the sleep-wake dynamics of the cardiac rhythm
,” Comput. Cardiol.
32
, 591
–594
(2005
).37.
M. T.
Bianchi
, N. A.
Eiseman
, S. S.
Cash
, J.
Mietus
, Ch.
Peng
, and R. J.
Thomas
, “Probabilistic sleep architecture models in patients with and without sleep apnea
,” J. Sleep Res.
21
, 330
–341
(2012
).38.
J. C.
Comte
, M.
Schatzman
, P.
Ravassard
, P. H.
Luppi
, and P. A.
Salin
, “A three states sleep–waking model
,” Chaos, Solitons Fractals
29
, 808
–881
(2006
).39.
J. W.
Kim
, J. S.
Lee
, P. A.
Robinson
, and D. U.
Jeong
, “Markov analysis of sleep dynamics
,” Phys. Rev. Lett.
102
, 178104
(2009
).40.
41.
C. C.
Lo
, L. N.
Amaral
, S.
Havlin
, P. C.
Ivanov
, T.
Penzel
, J. H.
Peter
, and H. E.
Stanley
, “Dynamics of sleep-wake transitions during sleep
,” Europhys. Lett.
57
, 625
–631
(2002
).42.
C. C.
Lo
, T.
Chou
, T.
Penzel
, T. E.
Scammell
, R. E.
Strecker
, H. E.
Stanley
, and P. C.
Ivanov
, “Common scale-invariant patterns of sleep–wake transitions across mammalian species
,” Proc. Natl. Acad. Sci.
101
, 17545
–17548
(2004
).43.
C. C.
Lo
, R. P.
Bartsch
, and P. C.
Ivanov
, “Asymmetry and basic pathways in sleep-stage transitions
,” Europhys. Lett.
102
, 10008
(2013
).44.
D.
Cysarz
, H.
Bettermann
, S.
Lange
, D.
Geue
, and P.
van Leeuwen
, “A quantitative comparison of different methods to detect cardiorespiratory coordination during nighttime sleep
,” BioMed. Eng. OnLine
3
, 44
(2004
).45.
H.
Bettermann
, D.
Cysarz
, and P.
van Leeuwen
, “Detecting cardiorespiratory coordination by respiratory pattern analysis of heart period dynamics—The musical rhythm approach
,” Int. J. Bifurcation Chaos
10
, 2349
–2360
(2000
).46.
R. P.
Bartsch
, A. Y.
Schumann
, J. W.
Kantelhardt
, T.
Penzel
, and P. C.
Ivanov
, “Phase transitions in physiologic coupling
,” Proc. Natl. Acad. Sci.
109
, 10181
–10186
(2012
).47.
A.
Bashan
, R. P.
Bartsch
, J. W.
Kantelhardt
, S.
Havlin
, and P. C.
Ivanov
, “Network physiology reveals relations between network topology and physiological function
,” Nat. Commun.
3
, 702
(2012
).48.
A. Y.
Schumann
, R. P.
Bartsch
, T.
Penzel
, P. C.
Ivanov
, and J. W.
Kantelhardt
, “Aging effects on cardiac and respiratory dynamics in healthy subjects across sleep stages
,” Sleep
33
, 943
–955
(2010
).49.
E.
Sforza
, C.
Jouny
, and V.
Ibanez
, “Cardiac activation during arousal in humans: Further evidence for hierarchy in the arousal response
,” Clin. Neurophysiol.
11
, 1611
–1619
(2000
).50.
M. A.
Woo
, W. G.
Stevenson
, D. K.
Moser
, R. B.
Trelease
, and R. M.
Harper
, “Patterns of beat-to-beat heart rate variability in advanced heart failure
,” Am. Heart J.
123
, 704
–710
(1992
).51.
J. J.
Żebrowski
, W.
Popławska
, and R.
Baranowski
, “Entropy, pattern entropy, and related methods for the analysis of data on the time intervals between heartbeats from 24-h electrocardiograms
,” Phys. Rev. E
50
, 4187
(1994
).52.
M.
Soliński
, J.
Gierałtowski
, and J. J.
Żebrowski
, “Modeling of human heart rate variability enhanced using stochastic sleep architecture properties
,” Comput. Cardiol.
41
, 513
–516
(2014
).53.
P. C.
Ivanov
, A.
Bunde
, L. N.
Amaral
, S.
Havlin
, J.
Fritsch-Yelle
, R. M.
Baeysky
, and A. L.
Goldberger
, “Sleep-wake differences in scaling behavior of the human heartbeat: Analysis of terrestrial and long-term space flight data
,” Europhys. Lett.
48
, 594
–600
(1999
).54.
P. C.
Ivanov
, “Scale-invariant aspects of cardiac dynamics across sleep stages and circadian phases
,” IEEE Eng. Med. Biol. Mag.
26
, 33
–37
(2007
).55.
J. W.
Kantelhardt
, Y.
Ashkenazy
, P. C.
Ivanov
, A.
Bunde
, S.
Havlin
, T.
Penzel
, and H. E.
Stanley
, “Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments
,” Phys. Rev. E
65
, 051908
(2002
).© 2016 AIP Publishing LLC.
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