Multifractal estimates of monofractality in RR-heart series in power spectrum ranges

Physica A: Statistical Mechanics and its Applications

Volumn 388, Issue 17, 2009, Pages 3486-3502

  Makowiec, Danuta ^a   Dudkowska, Aleksandra ^a   Gała̧ska, Rafał ^b   Rynkiewicz, Andrzej ^b  

^a UNIVERSITY OF GDA SK   (Poland)

^b MEDICAL UNIVERSITY OF GDANSK   (Poland)

Author keywords

Fractional Brownian motion; Heart rate variability; Multifractal analysis

Indexed keywords

ACTIVATION ANALYSIS; BROWNIAN MOVEMENT; HEART; POWER SPECTRUM; WAVELET TRANSFORMS;

FRACTIONAL BROWNIAN MOTION; HEART RATE VARIABILITY; MULTI-FRACTAL PROPERTY; MULTIFRACTAL ANALYSIS; MULTIFRACTAL CHARACTERISTICS; MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS; SYMPATHETIC NERVOUS SYSTEMS; WAVELET TRANSFORM MODULUS MAXIMA;

FRACTALS;

EID: 67349265151     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.05.005     Document Type: Article

References (44)

1. R.E. Klabunde, Cardiovascular physiology concepts, 2007. Accessible from http://www.cvphysiology.com
2. Heart rate variability. Standards of measurement, physiological interpretation, and clinical use. Eur. Heart J. 17 (1996) 354-381
3. De Jong M.J., and Randall D.C. Heart rate variability analysis in the assessment of autonomic function in heart failure. J. Cardiovasc. Nurs. 20 3 (2005) 186-195
4. Freneaux M.P. Autonomic changes in patients with heart failure and in post-myocardial infraction patients. Heart 90 11 (2004) 1248-1255
5. Toledo E., Pinhas I., Aravot D., Almog Y., and Akselrod S. Functional restitution of cardiac control in heart transplant patients. Am. J. Physiol. Regul. Integr. Comp. Phys. 280 (2002) R900-R908
6. Jackson G., Gibbs C.R., Davies M.K., and Lip G.Y.H. ABC of heart failure. Pathophysiology. British Med. J. 320 (2000) 167-176
7. Malik M. Heart Rate Variability and Baroreflex Sensitivity. 4th edition. In: Zipes D.P., and Jalife J. (Eds). Cardiac Electrophysiology. From Cell to Bedside (2004), Saunders
8. Gregory M.E., Cody R.J., Nuziata E., and Binkley P.F. Early left dysfunction elicits activation of sympathetic drive and attenuation of parasympathetic tone in paced canine model of congestive heart failure. Circulation 92 (1995) 551-561
9. Sandercock G.R.H., and Brodie D.A. The role of heart variability in prognosis for different modes of death in chronic heart failure. Pacing Clin. Electrophysiol. 29 8 (2006) 892
10. Beckers F., Verheyden B., and Aubert A.E. Aging and nonlinear heart rate control in healthy population. Am. J. Physiol. Heart Circ. Physiol. 290 (2006) H2560-H2570
11. Ivanov P.Ch., Rosenblum M.G., Peng C.-K., Mietus J., Havlin S., Stanley H.E., and Goldberger A.L. Scaling behavior of heartbeat intervals obtained by wavelet-based time-series analysis. Nature 383 (1999) 323-327
12. Ivanov P.Ch., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Stanley H.E., and Struzik Z.R. From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos 11 (2001) 641-652
13. Ivanov P.Ch., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Struzik Z.R., and Stanley H.E. Multifractality in human heartbeat dynamics. Nature 399 (1999) 461-465
14. Meyer M., and Stiedl O. Self-affine fractal variability of human heartbeat interval dynamics in health and disease. Eur. J. App. Physiol. 90 (2003) 305-316
15. Kotani K., Struzik Z.R., Takamasu K., Stanley H.E., and Yamamoto Y. Model for complex heart rate dynamics in health and diseases. Phys. Rev. E 72 (2005) 041904-1-8
16. Kiyono K., Struzik Z.R., Aoyagi N., Toga F., and Yammamoto Y. Phase transition in a healthy human heart rate. Phys. Rev. Lett. 95 (2005) 058101-1-4
17. Struzik Z.R., Hayano J., Sakata S., Kwak S., and Yamamoto Y. 1/f Scaling in heart rate requires antagonistic autonomic control. Phys. Rev. E 70 (2004) 050901-1-4(R)
18. Makowiec D., Gała̧ska R., Dudkowska A., Rynkiewicz A., and Zwierz M. Long-range dependencies in heart rate signals - Revisited. Physica A 369 (2006) 632-644
19. Gała̧ska R., Makowiec D., Dudkowska A., Koprowski A., Chlebus K., Wdowczyk-Szulc J., and Rynkiewicz A. Comparison of wavelet transform modulus maxima and multifractal detrended fluctuation analysis of heart rate in patients with systolic dysfunction of left ventricle. Ann. Noninvasive Electrocardiol. 13 (2008) 155-164
20. Kobayashi M., and Musha T. 1/f fluctuation of heartbeat period. IEEE Trans. Biomed. Eng. BME-29 (1982) 456-457
21. Peng C.K., Mietus J., Hausdorff J., Havlin S., Stanley H.E., and Goldberger A.L. Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Phys. Rev. Lett. 70 (1993) 1343-1347
22. Yamamoto Y., and Hughson R.L. On the fractal nature of heart rate variability in humans: Effects of data length and beta-adrenergic blockade. Am. J. Physiol. 266 (1994) R40-R49
23. Peng C.-K., Havlin S., Stanley H.E., and Goldberger A.L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5 1 (1995) 82-87
24. Cerutti S., Esposti F., Ferrario M., Sassi R., and Signorini M.G. Long-term invariant parameters obtained from 24-h Holter recordings: A comparison between different analysis techniques. Chaos 17 (2007) 015108-1-9
25. Ivanov P.Ch., Bunde A., Amaral L.A.N., Havlin S., Fritsch-Yelle J., Baewsky R.M., Stanley H.E., and Goldberger A.L. Sleep-wake differences in scaling behavior of human heartbeat: Analysis of terrestrial and long-term space flight data. Eurphys. Lett. 48 5 (1999) 594-600
26. Kantelhardt J.W., Ashkenazy Y., Ivanov P.Ch., Bunde A., Havlin S., Penzel T., Peter J.H., and Stanley H.E. Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments. Phys. Rev. E 65 (2002) 051908-1-6
27. Penzel T., Wessel N., Riedl M., Kantelhardt J.W., Rostig S., Glos M., Suhrbier A., Malberg H., and Fietze I. Cardiovascular and respiratory dynamics during normal and pathological sleep. Chaos 17 (2007) 015116-1-10
28. Riedi R.H. Multifractal processes. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theory and Applications (2001), Birkhäuser, Cambridge MA 625-716
29. Willinger W., Paxson V., Riedi R.H., and Taqqu M.S. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theory and Applications (2001), Birkhäuser, Cambridge MA 1-38
30. Oświȩcimka P., Kwapień J., and Drożdż S. Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E 74 (2006) 016103-1-17
31. Muzy J.F., Bacry E., and Arneodo A. Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E 47 (1993) 875-884
32. Arnedo A., Bacry E., and Muzy J.F. The thermodynamics of fractals revisited with wavelets. Physica A 213 (1995) 232-275
33. Lashermes B., Roux S.G., Abry P., and Jaffard S. Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders. Eur. Phys. J. B 61 (2008) 201-215
34. Kantelhardt J.W., Zschiegner S.A., Koscielny-Bunde E., Havlin S., Bunde A., and Stanley H.E. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316 (2002) 87-114
35. Scafetta N., Griffin L., and West B.J. Holder exponent spectra for human gait. Physica A 328 (2003) 561-583
36. Eke A., Herman P., Kocsis L., and Kozak L.R. Fractal characterization of complexity in temporal physiological signals. Phys. Meas. 23 (2002) R1-R38
37. Goldberger A.L., Amaral L.A.N., Glass L., Hausdorff J.M., Ivanov P.Ch., Mark R.G., Mietus J.E., Moody G.B., Peng C.-K., and Stanley H.E. PhysioBank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals. Circulation 101 23 (2000) e215-e220. http://circ.ahajournals.org/cgi/content/full/101/23/e215 [Circulation Electronic Pages; http://circ.ahajournals.org/cgi/content/full/101/23/e215]
38. RR series and MDFA software can be downloaded from http://iftia9.univ.gda.pl/~danka/DATA
39. Gneiting T., and Schlather M. Stochastic models that separate fractal dimension and Hurst effect. SIAM Rev. 64 (2004) 269-282
40. Amaral L.A.N., Ivanov P.Ch., Aoyagi N., Hidaka I., Tomono S., Goldberger A.L., Stanley H.E., and Yamamoto Y. Behavioral- independent features of complex heartbeat dynamics. Phys. Rev. Lett. 86 (2001) 6026-6029
41. Amaral L.A.N., Soares D.J.B., da Silva L.R., Lucena L.S., Saito M., Kumano H., Aoyagi N., and Yamamoto Y. Power law temporal auto-correlations in day-long record in human physical activity and their alternation with disease. Europhys. Lett. 66 3 (2004) 448-454
42. Togo F., Kiyono K., Struzik Z.R., and Yamamoto Y. Unique very low-frequency heart rate variability during deep sleep in humans. IEEE Trans. Biomed. Eng. 53 (2006) 28-34
43. J. Conove, http://www.johncon.com/. Copyright 1994-2005, John Conover, All Rights Reserved
44. Roach D., Sheldon A., Wilson W., and Sheldel R. Temporally localized contributions to measures of large-scale heart rate variability. Am. J. Physiol. Heart Circ. Physiol. 274 (1998) H1465-H1471