Power law temporal auto-correlations in day-long records of human physical activity and their alteration with disease

Europhysics Letters

Volumn 66, Issue 3, 2004, Pages 448-454

  Nunes Amaral, L A ^a   Bezerra Soares, D J ^b   Da Silva, L R ^b,c   Lucena, L S ^b   Saito, M ^d   Kumano, H ^d   Aoyagi, N ^e   Yamamoto, Y ^e,f  

^a Northwestern University   (United States)

^b FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

^c Boston University   (United States)

^d UNIVERSITY OF TOKYO HOSPITAL   (Japan)

^e UNIVERSITY OF TOKYO   (Japan)

^f JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442706344     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2003-10227-7     Document Type: Article

References (44)

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19. To our knowledge, the sole exception to this statement is a preliminary report suggesting the possibility that activity time series of some manic depressive patients may show fractal correlations (see SELZ K. A., MANDELL A. J., ANDERSON C. R., SMOTHERMAN W. P. and TEICHER M. H., Fractals, 3 (1995) 893).
20. The CR protocol was originally used in chronobiology research to investigate endogenous circadian rhythms as a means of minimizing environmental and behavioral influences (CZEISLER C. A., ALLAN J. S. and STROGATZ S. H., Science, 233 (1986) 667; CZEISLER C. A. et al., Science, 244 (1989) 1328; MILLS J. N., MINORS D. S. and WATERHOUSE J. M., J. Physiol. (London), 285 (1978) 455). Subjects were instructed to keep their regular sleep schedules (00:00-00:20h and 07:00-09:00h for sleep onset and wake-up, respectively) during the week prior to the study. They were required to refrain from vigorous exercise or alcohol consumption during a week prior to testing, when they reported to the laboratory at about 08:00 h after an overnight fast. Data collection started at 09:00-11:30 h, and subjects were kept awake for 27 h in a constant semi-recumbent posture with minimal physical activity. They were allowed to work on a laptop computer, read, listen to the radio, and talk quietly to the staff, in the controlled laboratory environment (temperature: 24-25°, light intensity: < 250 lx). Isocaloric meals were given every 2 h to minimize dietary-induced changes in heart rate. As a control, the data were also collected for each of the 7 subjects -with the same experimental settings as for CR-during usual activities of daily living, but without vigorous exercise or alcohol consumption.
21. The CR protocol was originally used in chronobiology research to investigate endogenous circadian rhythms as a means of minimizing environmental and behavioral influences (CZEISLER C. A., ALLAN J. S. and STROGATZ S. H., Science, 233 (1986) 667; CZEISLER C. A. et al., Science, 244 (1989) 1328; MILLS J. N., MINORS D. S. and WATERHOUSE J. M., J. Physiol. (London), 285 (1978) 455). Subjects were instructed to keep their regular sleep schedules (00:00-00:20h and 07:00-09:00h for sleep onset and wake-up, respectively) during the week prior to the study. They were required to refrain from vigorous exercise or alcohol consumption during a week prior to testing, when they reported to the laboratory at about 08:00 h after an overnight fast. Data collection started at 09:00-11:30 h, and subjects were kept awake for 27 h in a constant semi-recumbent posture with minimal physical activity. They were allowed to work on a laptop computer, read, listen to the radio, and talk quietly to the staff, in the controlled laboratory environment (temperature: 24-25°, light intensity: < 250 lx). Isocaloric meals were given every 2 h to minimize dietary-induced changes in heart rate. As a control, the data were also collected for each of the 7 subjects -with the same experimental settings as for CR-during usual activities of daily living, but without vigorous exercise or alcohol consumption.
22. The CR protocol was originally used in chronobiology research to investigate endogenous circadian rhythms as a means of minimizing environmental and behavioral influences (CZEISLER C. A., ALLAN J. S. and STROGATZ S. H., Science, 233 (1986) 667; CZEISLER C. A. et al., Science, 244 (1989) 1328; MILLS J. N., MINORS D. S. and WATERHOUSE J. M., J. Physiol. (London), 285 (1978) 455). Subjects were instructed to keep their regular sleep schedules (00:00-00:20h and 07:00-09:00h for sleep onset and wake-up, respectively) during the week prior to the study. They were required to refrain from vigorous exercise or alcohol consumption during a week prior to testing, when they reported to the laboratory at about 08:00 h after an overnight fast. Data collection started at 09:00-11:30 h, and subjects were kept awake for 27 h in a constant semi-recumbent posture with minimal physical activity. They were allowed to work on a laptop computer, read, listen to the radio, and talk quietly to the staff, in the controlled laboratory environment (temperature: 24-25°, light intensity: < 250 lx). Isocaloric meals were given every 2 h to minimize dietary-induced changes in heart rate. As a control, the data were also collected for each of the 7 subjects -with the same experimental settings as for CR-during usual activities of daily living, but without vigorous exercise or alcohol consumption.
23. This finding confirms the basic assumption behind the use of the CR protocol -i.e., that the CR protocol allows the investigation of endogenous rhythms through the minimization of environmental and behavioral influences.
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29. Each subject gave informed consent to participate in this study after the test protocol was fully described. This study was reviewed and approved by the ethics committee of the Graduate School of Education of The University of Tokyo.
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33. By adjusting the order of the DFA method, one is able to avoids spurious detection of correlations that are artifacts of polynomial trends (ASHKENAZY Y. et al., Phys. Rev. Lett., 86 (2001) 1900; Hu K. et al., Phys. Rev. E, 64 (2001) 011114).
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36. We distinguish between voluntary physical activity, such as walking, sitting, etc., and involuntary physical activity, such as body tremor, balance adjustment, etc.
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38. Here, we do not analyze in detail the absolute activity level. The reason is that the use of absolute activity counts recorded by actigraphs for analysis of human activity has raised a number of serious concern in the scientific literature (see ref. [18] for details). In contrast, the relative changes measured by the accelerometer, which is the quantity we are concerned with in this letter, are not hindered by such methodological concerns [18].
39. Each patient gave informed consent to participate in this study after the test protocol was fully described. This study was reviewed and approved by the ethics committee of The University of Tokyo Hospital. The method of data collection was the same as that for healthy subjects.
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42. Multifractal signals-such as those generated by binomial multiplicative processes or turbulent fluctuations-can be decomposed into many subsets characterized by different local Hurst exponents h, which quantify the local singular behavior and thus relate to the local fractal properties of the time series (VICSEK T., Fractal Growth Phenomena, 2nd edition (World Scientific, Singapore) 1993).
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44. Physiologic signals and the algorithms for their analysis are freely available at the PhysioNet website (http://www.physionet.org).