Skip to main content
Log in

Scaling exponent values as an ordinary function of the ratio of very low frequency to high frequency powers in heart rate variability over various sleep stages

  • Sleep Breathing Physiology and Disorders • Original Article
  • Published:
Sleep and Breathing Aims and scope Submit manuscript

Abstract

Purpose

To assess the physiological meanings of the detrended fluctuation analysis (DFA) slope α and its relationship to spectral measures in heart rate variability, this study investigated changes of α and its corresponding spectral measures over various night-sleep stages.

Methods

The overall DFA α and natural-logarithm-transformed power values of the spectral parameters ln[high-frequency (HF)], ln[low-frequency (LF)], and ln[very-low-frequency (VLF)], and their relationship from one 5-min proper electrocardiography segment in each of pre-sleep-wakefulness (AWK), non-rapid eye movement stage 2 (N2), slow-wave (N3), the first and the latest rapid-eye movement sleep (REM1, and REM2), were computed in 93 otherwise healthy males (44.1 ± 7.7 years.) with wide-ranged apnea-hypopnea, periodic-limb movement and arousal indices (19.0 ± 20.9, 4.7 ± 9.9, and 10.7 ± 18.2 h, respectively).

Results

While ln(HF) dipped from AWK, N2, and N3 to REM1 then rebounded to the origin level at REM2, ln(VLF) dipped from AWK to N2, N3 trough, and then surged to levels surpassing AWKs and N2s at REM1 and REM2. ln(LF/HF), ln(VLF/HF), and α dipped from AWK and N2 to N3 trough, surged to levels surpassing AWKs, and N2s at REM1 then became attenuated at REM2. By general linear modeling, the relationship between α and the corresponding spectral values can be seen over various stages as α = b 0 + 0.147 × ln(VLF/HF) (R 2 = 0.766), regardless of age and sleep-sympathoexcitatory episodes.

Conclusion

The REM sleep attenuations appeared in ln(HF) and its derivatives, such as ln(LF/HF), ln(VLF/HF), and the overall DFA slope α values. The quantitative function of ln(VLF/HF) describes the α values constantly for overnight sleep stages, and it is not affected by age, LF, PLM, and AHI. Our findings therefore suggest that in sleep studies with spectral HRV measures, ln(VLF/HF) as a surrogate of the overall DFA slope α should be calculated at the same time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Zipes DP, Wellens HJ (1998) Sudden cardiac death. Circulation 98:2334–2351

    Article  CAS  PubMed  Google Scholar 

  2. Malik M (1996) Heart rate variability: standards of measurement, physiological interpretation and clinical use task force of the european society of cardiology and the north american society of pacing and electrophysiology. Circulation 93:1043–1065

    Article  Google Scholar 

  3. Taylor JA, Carr DL, Myers CW, Eckberg DL (1998) Mechanisms underlying very-low-frequency RR-interval oscillations in humans. Circulation 98:547–555

    Article  CAS  PubMed  Google Scholar 

  4. Berlad II, Shlitner A, Ben-Haim S, Lavie P (1993) Power spectrum analysis and heart rate variability in stage 4 and REM sleep: evidence for state-specific changes in autonomic dominance. J Sleep Res 2:88–90

    Article  PubMed  Google Scholar 

  5. Bonsignore MR, Romano S, Marrone O, Chiodi M, Bonsignore G (1997) Different heart rate patterns in obstructive apneas during NREM sleep. Sleep 20:1167–1174

    CAS  PubMed  Google Scholar 

  6. Sforza E, Pichot V, Barthelemy JC, Haba-Rubio J, Roche F (2005) Cardiovascular variability during periodic leg movements: a spectral analysis approach. Clin Neurophysiol 116:1096–1104

    Article  PubMed  Google Scholar 

  7. Huikuri HV, Perkiomaki JS, Maestri R, Pinna GD (2009) Clinical impact of evaluation of cardiovascular control by novel methods of heart rate dynamics. Philos Trans A Math Phys Eng Sci 367:1223–1238

    Article  PubMed  Google Scholar 

  8. Francis DP, Willson K, Georgiadou P, Wensel R, Davies LC, Coats A, et al. (2002) Physiological basis of fractal complexity properties of heart rate variability in man. J Physiol 542:619–629

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Beckers F, Verheyden B, Aubert AE (2006) Aging and nonlinear heart rate control in a healthy population. Am J Physiol Heart Circ Physiol 290:H2560–H2570

    Article  CAS  PubMed  Google Scholar 

  10. Hu K, Ivanov P, Hilton MF, Chen Z, Ayers RT, Stanley HE, et al. (2004) Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior. Proc Natl Acad Sci U S A 101:18223–18227

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Hu K, Scheer FA, Buijs RM, Shea SA (2008) The circadian pacemaker generates similar circadian rhythms in the fractal structure of heart rate in humans and rats. Cardiovasc Res 80:62–68

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Takabatake N, Nakamura H, Minamihaba O, Inage M, Inoue S, Kagaya S, et al. (2001) A novel pathophysiologic phenomenon in cachexic patients with chronic obstructive pulmonary disease: the relationship between the circadian rhythm of circulating leptin and the very low-frequency component of heart rate variability. Am J Respir Critical Care Med 163:1314–1319

    Article  CAS  Google Scholar 

  13. Burgess HJ, Trinder J, Kim Y, Luke D (1997) Sleep and circadian influences on cardiac autonomic nervous system activity. Am J Physiol 273:H1761–H1768

    CAS  PubMed  Google Scholar 

  14. Hilton MF, Umali MU, Czeisler CA, Wyatt JK, Shea SA (2000) Endogenous circadian control of the human autonomic nervous system. Comput Cardiol 27:197–200

    CAS  PubMed  Google Scholar 

  15. Schumann AY, Bartsch RP, Penzel T, Ivanov P, Kantelhardt JW (2010) Aging effects on cardiac and respiratory dynamics in healthy subjects across sleep stages. Sleep 33:943–955

    PubMed  PubMed Central  Google Scholar 

  16. Kuo TB, Yang CC (2004) Scatterplot analysis of EEG slow-wave magnitude and heart rate variability: an integrative exploration of cerebral cortical and autonomic functions. Sleep 27:648–656

    PubMed  Google Scholar 

  17. Tan CO, Cohen MA, Eckberg DL, Taylor JA (2009) Fractal properties of human heart period variability: physiological and methodological implications. J Physiol 587:3929–3941

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Penzel T, Kantelhardt JW, Lo CC, Voigt K, Vogelmeier C (2003) Dynamics of heart rate and sleep stages in normals and patients with sleep apnea. Neuropsychopharmacol Off Publ Am College Neuropsychopharmacol 28(Suppl 1):S48–S53

    Article  Google Scholar 

  19. Heitmann A, Huebner T, Schroeder R, Perz S, Voss A (2011) Multivariate short-term heart rate variability: a pre-diagnostic tool for screening heart disease. Med Biol Eng Comput 49:41–50

    Article  PubMed  Google Scholar 

  20. Deboer T, Vansteensel MJ, Detari L, Meijer JH (2003) Sleep states alter activity of suprachiasmatic nucleus neurons. Nat Neurosci 6:1086–1090

    Article  CAS  PubMed  Google Scholar 

  21. Ting H, Lo HS, Chang SY, Chung AH, Kuan PC, Yuan SC, et al. (2009) Post- to pre-overnight sleep systolic blood pressures are associated with sleep respiratory disturbance, pro-inflammatory state and metabolic situation in patients with sleep-disordered breathing. Sleep Med 10:720–725

    Article  PubMed  Google Scholar 

  22. Askew EW (2002) Work at high altitude and oxidative stress: antioxidant nutrients. Toxicology 180:107–119

    Article  CAS  PubMed  Google Scholar 

  23. Bunde A, Havlin S, Kantelhardt JW, Penzel T, Peter JH, Voigt K (2000) Correlated and uncorrelated regions in heart-rate fluctuations during sleep. Phys Rev Lett 85:3736–3739

    Article  CAS  PubMed  Google Scholar 

  24. Penzel T, Wessel N, Riedl M, Kantelhardt JW, Rostig S, Glos M, et al. (2007) Cardiovascular and respiratory dynamics during normal and pathological sleep. Chaos 17:015116

    Article  PubMed  Google Scholar 

  25. da Silva EL, Pereira R, Reis LN, Pereira VL Jr., Campos LA, Wessel N, et al. (2015) Heart rate detrended fluctuation indexes as estimate of obstructive sleep apnea severity. Medicine 94:e516

  26. Kryger MH, Roth T, Dement WC, Borbély AA (2011) Sleep Homeostasis and Models of Sleep Regulation. In Principles and Practice of Sleep Medicine 5th edn. 431–44.

  27. Hu K, Van Someren EJ, Shea SA, Scheer FA (2009) Reduction of scale invariance of activity fluctuations with aging and Alzheimer’s disease: involvement of the circadian pacemaker. Proc Natl Acad Sci U S A 106:2490–2494

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. van Eekelen AP, Houtveen JH, Kerkhof GA (2004) Circadian variation in base rate measures of cardiac autonomic activity. Eur J Appl Physiol 93:39–46

    Article  PubMed  Google Scholar 

  29. Fleisher LA, Frank SM, Sessler DI, Cheng C, Matsukawa T, Vannier CA (1996) Thermoregulation and heart rate variability. Clin Sci (Lond) 90:97–103

    Article  CAS  Google Scholar 

  30. Krauchi K (2007) The human sleep-wake cycle reconsidered from a thermoregulatory point of view. Physiol Behav 90:236–245

    Article  PubMed  Google Scholar 

  31. Di Rienzo M, Parati G, Castiglioni P, Omboni S, Ferrari AU, Ramirez AJ, et al. (1991) Role of sinoaortic afferents in modulating BP and pulse-interval spectral characteristics in unanesthetized cats. Am J Physiol 261:H1811–H1818

    PubMed  Google Scholar 

  32. Bigger JT Jr., Fleiss JL, Steinman RC, Rolnitzky LM, Kleiger RE, Rottman JN (1992) Frequency domain measures of heart period variability and mortality after myocardial infarction. Circulation 85:164–171

    Article  PubMed  Google Scholar 

  33. Bigger JT, Fleiss JL, Rolnitzky LM, Steinman RC (1993) The ability of several short-term measures of RR variability to predict mortality after myocardial infarction. Circulation 88:927–934

    Article  CAS  PubMed  Google Scholar 

  34. Penzel T, Kantelhardt JW, Grote L, Peter JH, Bunde A (2003) Comparison of detrended fluctuation analysis and spectral analysis for heart rate variability in sleep and sleep apnea. IEEE Trans on Biomed Eng 50:1143–1150

    Article  Google Scholar 

Download references

Acknowledgments

We thank Dr. Tim Williams for his support throughout the editing process.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hua Ting.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Ethical approval

All procedures performed in studies involving human.

participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Funding

The National Science Council, Taiwan provided financial support in the form of 98–2314-B-040-001-MY3 funding.

Taiwan Department of Health Clinical Trial and Research Center of Excellence provided financial support in the form of DOH102-TD-B-111-004 funding.

Additional information

Ren-Jing Huang, Ching-Hsiang Lai and Shin-Da Lee this authors contributed equally

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, RJ., Lai, CH., Lee, SD. et al. Scaling exponent values as an ordinary function of the ratio of very low frequency to high frequency powers in heart rate variability over various sleep stages. Sleep Breath 20, 975–985 (2016). https://doi.org/10.1007/s11325-016-1320-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11325-016-1320-5

Keywords

Navigation