Skip to main content
SpringerLink
Log in

Applying fractal analysis to short sets of heart rate variability data

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

The aim of this study was to explore the interchangeability of fractal scaling exponents derived from short- and long-term recordings of real and synthetic data. We compared the α1 exponents as obtained by detrended fluctuation analysis from RR-interval series (9 am to 6 pm) of 54 adults in normal sinus rhythm, and the α1 estimated from shorted segments of these series involving only 50, 100, 200 and 300 RR intervals. Three series of synthetic data were also analysed. The principal finding of this study is the lack of individual agreement between α1 derived from long and short segments of HRV data as indicated by the existence of bias and low intraclass correlation coefficient (r i  = 0.158). The extent of variation in the estimation of α1 from real data does not only appear related to segments’ length, but also to different dynamics among subjects or lack of uniform scaling behaviour. However, we did find statistical agreement between the means of α1 exponents from long and short segments, even for segments involving just 50 RR intervals. According to results of synthetic series, the 95% confidence interval found for the variation of α1 using segments with 300 samples is [−0.1783 + 0.1828]. Caution should be taken concerning the use of short segments to obtain representative exponents of fractal RR dynamics; a circumstance not fully considered in several studies.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Amaral LAN, Ivanov PC, Aoyagi N, Hidaka I, Tomono S, Goldberger AL, Stanley HE, Yamamoto Y (2001) Behavioral-independent features of complex heartbeats dynamics. Phys Rev Lett 86(26):6026–6029

    Article  Google Scholar 

  2. Bassingthwaighte JB, Raymond GM (1995) Evaluation of the dispersional analysis method for fractal time series. Ann Biomed Eng 23:491–505

    Article  Google Scholar 

  3. Baumert M, Wessel N, Schirdewan A, Voss A, Abbott D (2007) Scaling characteristics of heart rate time series before the onset of ventricular tachycardia. Ann Biomed Eng 35:201–207

    Article  Google Scholar 

  4. Bernaola-Galvan P, Ivanov PC, Amaral LAN, Stanley HE (2001) Scale-invariance in the nonstationarity of human heart rate. Phys Rev Lett 87:168105

    Article  Google Scholar 

  5. Bigger JT, Fleiss JL, Steinman RC, Rolnitzky LM, Schneider WJ, Stein PK (1995) RR variability in healthy, middle-aged persons compared with patients with chronic heart disease or recent acute myocardial infarction. Circulation 91:1936–1943

    Google Scholar 

  6. Bland JM, Altman DG (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 8:307–310

    Google Scholar 

  7. Buchman TG (2002) The community of the self. Nature 420:246–251

    Article  Google Scholar 

  8. 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  Google Scholar 

  9. Chen Z, Ivanov PC, Hu K, Stanley HE (2002) Effect of nonstationarities on detrended fluctuation analysis. Phys Rev E 65:041107

    Article  Google Scholar 

  10. Echeverria JC, Aguilar SD, Ortiz MR, Alvarez-Ramirez J, Gonzalez-Camarena R (2006) Comparison of RR-interval scaling exponents derived from long and short segments at different wake periods. Physiol Meas 27:N19–N25

    Article  Google Scholar 

  11. Echeverria JC, Woolfson MS, Crowe JA, Hayes-Gill BR, Pieri JF, Spencer CJ, James DK (2004) Does fractality in heart rate variability indicate the development of fetal neural processes? Phys Lett A 331:225–230

    Article  MATH  Google Scholar 

  12. Eke A, Herman P, Kocsis L, Kozak LR (2002) Fractal characterization of complexity in temporal physiological signals. Physiol Meas 23:R1–R38

    Article  Google Scholar 

  13. Eke A, Herman P, Bassingthwaighte JB, Raymond GM, Percival DB, Cannon M, Balla I, Ikrenyi C (2000) Physiological time series: distinguishing fractal noises from motions. Eur J Physiol 439:403–415

    Article  Google Scholar 

  14. Fischer R, Akay M (2002) Improved estimators for fractional Brownian motion via the expectation–maximization algorithm. Med Eng Phys 24:77–83

    Article  Google Scholar 

  15. Fischer R, Akay M, Castiglioni P, Rienzo MD (2003) Multi- and monofractal indices of short-term heart rate variability. Med Biol Eng Comput 41:543–549

    Article  Google Scholar 

  16. Francis DP, Willson K, Georgiadou P, Wensel R, Davies LC, Coats A, Piepoli M (2002) Physiological basis of fractal complexities properties of heart rate variability in man. Journal of Physiology 542:619–629

    Article  Google Scholar 

  17. Goldberger AL (1996) Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet 347:1312–1314

    Article  Google Scholar 

  18. Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, Mietus JE, Moody GB, Peng CK, Stanley HE (2000) Physiobank, physiotoolkit and physionet. Circulation 101:e215–e220

    Google Scholar 

  19. Goldberger AL, Peng CK, Lipsitz LA (2002) What is physiologic complexity and how does it change with aging and disease? Neurobiol Aging 23:23–26

    Article  Google Scholar 

  20. Hautala AJ, Makikallio TH, Seppanen T, Huikuiri HV, Tulppo MP (2003) Short-term correlation properties of R–R interval dynamics at different exercise intensity levels. Clin Physiol Funct Imaging 23:215–223

    Article  Google Scholar 

  21. Hayano J, Sakakibara Y, Yamada M, Kamiya T, Fujinami T, Yokoyama M, Watanabe Y, Takata K (1990) Diurnal variations in vagal and sympathetic cardiac control. Am J Physiol Heart Circ Physiol 280:H642–H646

    Google Scholar 

  22. Heneghan C, McDarby G (2000) Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Phys Rev E 62:6103–6110

    Article  Google Scholar 

  23. Hu K, Ivanov PC, Chen Z, Carpena P, Stanley HE (2001) Effect of trends on detrended fluctuation analysis. Phys Rev E 64:011–114

    Google Scholar 

  24. Huang HH, Lee YH, Chan HL, Wang YP, Huang CH, Fan SZ (2008) Using a short-term parameter of heart rate variability to distinguish awake from isoflurane anesthetic states. Med Biol Eng Comput 46:977–984

    Article  Google Scholar 

  25. Hu K, Ivanov PC, Hilton MF, Chen Z, Ayers T, H. E. Stanley HE (2004) Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior. In: Proceedings of the National Academy of Sciences 101:18223–18227

  26. Huikuri HV, Makikallio TH, Peng CK, Goldberger AL, Hintze U, Moller M (2000) Fractal correlation properties of R–R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction. Circulation 101:47–53

    Google Scholar 

  27. Ivanov PC, Amaral LAN, Goldberger AL, Havlin S, Rosenblum MG, Struzik ZR, Stanley HE (1999) Multifractality in human heartbeat dynamics. Nature 399:461–465

    Article  Google Scholar 

  28. Ivanov PC, Bunde A, Amaral LAN, Havlin S, Fritsch-Yelle J, Baevsky RM, Stanley HE, Goldberger AL (1999) Sleep-wake differences in scaling behaviour of the human heartbeat: analysis of terrestrial and long-term space flight. Europhys Lett 48:594–600

    Article  Google Scholar 

  29. Ivanov PC, Nunes LA, Golberger AL, Halvin S, Rosenblum MG, Stanley HE, Struzik ZR (2001) From 1/f noise to multifractal cascades in heartbeats dynamics. Chaos 11:641–652

    Article  MATH  Google Scholar 

  30. Lee J, Koh D, Ong CN (1989) Statistical evaluation of agreement between two methods for measuring a quantitative variable. Comput Biol Med 19:61–70

    Article  Google Scholar 

  31. Mahon NG, Hedman AE, Padula M, Gang Y, Savelieva I, Waktare JEP, Malik MM, Huikuri HV, McKenna WJ (2002) Fractal correlation properties of R–R interval dynamics in asymptomatic relatives of patients with dilated cardiomyopathy. Eur J Heart Fail 4:151–8

    Article  Google Scholar 

  32. Mietus JE, Peng Henry I, Goldsmith RL, Goldberger AL (2002) The pNNx files: re-examining a widely heart rate variability measure. Heart 88:378–380

    Article  Google Scholar 

  33. Ortiz MR, Aguilar SD, Alvarez-Ramirez J, Martinez A, Vargas-Garcia C, Gonzalez-Camarena R, Echeverria JC (2006) Prenatal RR fluctuations dynamics: detecting fetal short-range fractal correlations. Prenatal Diagnosis 26:1241–1247

    Article  Google Scholar 

  34. Parati G0, Mancia G, Rienzo MD, Castiglioni P, Taylor JA, Studinger P (2006) Point:counterpoint: cardiovascular variability is/is not an index of autonomic control of circulation. J Appl Physiol 101:676–682

    Article  Google Scholar 

  35. Peng CK, Havlin S, Stanley HE, Goldberger AL (1995) Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5:82–87

    Article  Google Scholar 

  36. 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 Biomed Eng 50:1143–1151

    Article  Google Scholar 

  37. Pikkujamsa SM, Makikallio TH, Huikuri HV (2001) Determinants and interindividual variation of R–R interval dynamics in healthy middle-aged sub jects. Am J Physiol Heart Circ Physiol 280:H1400–H1406

    Google Scholar 

  38. Platisa MM, Gal V (2006) Reflection of heart rate regulation on linear and nonlinear heart rate variability measures. Physiol Meas 27:145–154

    Article  Google Scholar 

  39. Platisa MM, Mazic S, Nestorovic Z, Gal V (2008) Complexity of heartbeat interval series in young healthy trained and untrained men. Physiol Meas 29:439–450

    Article  Google Scholar 

  40. Schmitt DT, Ivanov PC (2007) Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly. Am J Physiol Regul Integr Comp Physiol 293:R1923–R1937

    Google Scholar 

  41. Task Force of the European Society of Cardiology, The North American Society of Pacing and Electrophysiology (1996) Task-force: heart rate variability, standards of measurements, physiological interpretation, and clinical use. Eur Heart J 17:354–381

    Google Scholar 

  42. Togo F, Yamamoto Y (2000) Decreased fractal component of human heart rate variability during non-rem sleep. Am J Physiol Heart Circ Physiol 280:H17–H21

    Google Scholar 

  43. Tulppo MP, Hughson RL, Makikallio TH, Airaksinen KEJ, Seppamen T, Huikuri HV (2001) Effects of exercise and passive head-up tilt on fractal and complexity properties of heart rate dynamics. Am J Physiol Heart Circ Physiol 280:H1081–H1087

    Google Scholar 

  44. Tulppo MP, Kiviniemi AM, Hautala AJ, Kallio M, Seppanen T, Makikallio TH, Heikki V, Huikuri HV (2005) Physiological background of the loss of fractal heart rate dynamics. Circulation 112:314–319

    Article  Google Scholar 

  45. Tulppo MP, Hautala AJ, Kallio M, Seppanen T, Makikallio TH, Huikuri HV (2003) Effects of aerobic training on heart rate dynamics in sedentary subjects. J Appl Physiol 95:364–372

    Google Scholar 

  46. Yamamoto Y, Hughson RL (1994) On the fractal nature of heart rate variability in humans: effects of data length and β-adrenergic blockade. Am J Physiol Regul Integr Comp Physiol 266:R40–R49

    Google Scholar 

  47. Willson K, Francis DP (2003) A direct analytical demonstration of the essential equivalence of detrended fluctuation analysis and spectral analysis of RR interval variability. Physiol Meas 24:N1–7

    Article  Google Scholar 

  48. Willson K, Francis DP, Wensel R, Coats AJS, Parker KH (2002) Relationship between detrended fluctuation analysis and spectral analysis of heart-rate variability. Physiol Meas 23:385–401

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Universidad Autónoma Metropolitana-Izt., San Rafael Atlixco #186, 09340, Mexico City, Mexico

    M. A. Peña, J. C. Echeverría & M. T. García

  2. Health Science Department, Universidad Autónoma Metropolitana-Izt., San Rafael Atlixco #186, 09340, Mexico City, Mexico

    R. González-Camarena

Authors
  1. M. A. Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. C. Echeverría
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. T. García
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. González-Camarena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Peña.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peña, M.A., Echeverría, J.C., García, M.T. et al. Applying fractal analysis to short sets of heart rate variability data. Med Biol Eng Comput 47, 709–717 (2009). https://doi.org/10.1007/s11517-009-0436-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-009-0436-1

Keywords

Search

Navigation