×

From \(1/f\) noise to multifractal cascades in heartbeat dynamics. (English) Zbl 0990.92024

Summary: We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiological signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales.
We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals.

MSC:

92C55 Biomedical imaging and signal processing
82D99 Applications of statistical mechanics to specific types of physical systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1111/j.1749-6632.1987.tb48734.x · doi:10.1111/j.1749-6632.1987.tb48734.x
[2] DOI: 10.1109/TBME.1982.324972 · doi:10.1109/TBME.1982.324972
[3] DOI: 10.1103/PhysRevLett.70.1343 · doi:10.1103/PhysRevLett.70.1343
[4] Hausdorff J. M., J. Appl. Physiol. 80 pp 1448– (1996)
[5] DOI: 10.1103/PhysRevE.59.5970 · doi:10.1103/PhysRevE.59.5970
[6] DOI: 10.1103/PhysRevE.59.5970 · doi:10.1103/PhysRevE.59.5970
[7] DOI: 10.1063/1.165990 · doi:10.1063/1.165990
[8] DOI: 10.1007/BF00198960 · doi:10.1007/BF00198960
[9] DOI: 10.1111/j.1540-8167.1994.tb01300.x · doi:10.1111/j.1540-8167.1994.tb01300.x
[10] DOI: 10.1063/1.166090 · doi:10.1063/1.166090
[11] DOI: 10.1038/383323a0 · doi:10.1038/383323a0
[12] DOI: 10.1073/pnas.93.6.2608 · Zbl 0851.92006 · doi:10.1073/pnas.93.6.2608
[13] DOI: 10.1038/39043 · doi:10.1038/39043
[14] DOI: 10.1103/PhysRevE.47.875 · doi:10.1103/PhysRevE.47.875
[15] DOI: 10.1038/20924 · doi:10.1038/20924
[16] DOI: 10.1126/science.267326 · Zbl 1383.92036 · doi:10.1126/science.267326
[17] Wolf M. M., Med. J. Australia 2 pp 52– (1978)
[18] DOI: 10.1126/science.6166045 · doi:10.1126/science.6166045
[19] DOI: 10.1063/1.166141 · doi:10.1063/1.166141
[20] DOI: 10.1016/S0378-4371(97)00522-0 · doi:10.1016/S0378-4371(97)00522-0
[21] DOI: 10.1103/PhysRevLett.86.1900 · doi:10.1103/PhysRevLett.86.1900
[22] Kitney R. I., Automedica 4 pp 141– (1982)
[23] DOI: 10.1016/S0140-6736(96)90948-4 · doi:10.1016/S0140-6736(96)90948-4
[24] DOI: 10.1103/PhysRevLett.61.1438 · doi:10.1103/PhysRevLett.61.1438
[25] DOI: 10.1161/01.RES.29.5.437 · doi:10.1161/01.RES.29.5.437
[26] DOI: 10.1209/epl/i1998-00366-3 · doi:10.1209/epl/i1998-00366-3
[27] P. Bernaola-Galvan, P. Ch. Ivanov, L. A. N. Amaral, and H. E. Stanley, ”Scale-invariance in the nonstationarity of physiological signals” (http://xxx.lanl.gov/cond-mat/0005284).
[28] DOI: 10.1103/PhysRevLett.85.1342 · doi:10.1103/PhysRevLett.85.1342
[29] DOI: 10.1103/PhysRevE.49.1685 · doi:10.1103/PhysRevE.49.1685
[30] DOI: 10.1103/PhysRevE.64.011114 · doi:10.1103/PhysRevE.64.011114
[31] DOI: 10.1103/PhysRevE.51.5084 · doi:10.1103/PhysRevE.51.5084
[32] DOI: 10.1016/S0006-3495(93)81290-6 · doi:10.1016/S0006-3495(93)81290-6
[33] DOI: 10.1016/S0006-3495(94)80455-2 · doi:10.1016/S0006-3495(94)80455-2
[34] Taqqu M. S., Fractals 3 pp 185– (1996)
[35] DOI: 10.1016/0002-9149(90)90308-N · doi:10.1016/0002-9149(90)90308-N
[36] DOI: 10.1016/0002-9149(91)90653-3 · doi:10.1016/0002-9149(91)90653-3
[37] DOI: 10.1209/epl/i1999-00525-0 · doi:10.1209/epl/i1999-00525-0
[38] DOI: 10.1016/0002-8703(94)90033-7 · doi:10.1016/0002-8703(94)90033-7
[39] DOI: 10.1103/PhysRevLett.85.3736 · doi:10.1103/PhysRevLett.85.3736
[40] DOI: 10.1038/378554a0 · doi:10.1038/378554a0
[41] Hurst H. E., Trans. Am. Soc. Civ. Eng. 116 pp 770– (1951)
[42] DOI: 10.1142/S0218348X00000184 · doi:10.1142/S0218348X00000184
[43] DOI: 10.1142/S0218348X0100049X · doi:10.1142/S0218348X0100049X
[44] DOI: 10.1088/0305-4470/24/15/010 · doi:10.1088/0305-4470/24/15/010
[45] DOI: 10.1142/S0218127494000204 · Zbl 0807.58032 · doi:10.1142/S0218127494000204
[46] DOI: 10.1103/PhysRevLett.86.6026 · doi:10.1103/PhysRevLett.86.6026
[47] DOI: 10.1103/PhysRevLett.81.2388 · doi:10.1103/PhysRevLett.81.2388
[48] DOI: 10.1103/PhysRevLett.59.1424 · doi:10.1103/PhysRevLett.59.1424
[49] DOI: 10.1038/335405a0 · doi:10.1038/335405a0
[50] DOI: 10.1016/S0022-5193(05)80127-4 · doi:10.1016/S0022-5193(05)80127-4
[51] DOI: 10.1016/S0167-2789(97)00229-7 · Zbl 0932.92024 · doi:10.1016/S0167-2789(97)00229-7
[52] DOI: 10.1103/PhysRevLett.86.1650 · doi:10.1103/PhysRevLett.86.1650
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.