Decreased Fractal Correlation in Diurnal Physical Activity in Chronic Fatigue Syndrome

K. Ohashi; G. Bleijenberg; S. van der Werf; J. Prins; L. A. N. Amaral; B. H. Natelson; Y. Yamamoto

doi:10.1055/s-0038-1633418

Methods of Information in Medicine, Table of Contents

Methods Inf Med 2004; 43(01): 26-29
DOI: 10.1055/s-0038-1633418

Original Article

Schattauer GmbH

Decreased Fractal Correlation in Diurnal Physical Activity in Chronic Fatigue Syndrome

Authors

K. Ohashi

¹Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, Japan
G. Bleijenberg

²The Netherlands Fatigue Research Group Nijmegen, Department of Medical Psychology and Internal Medicine, University Hospital Nijmegen, Nijmegen, The Netherlands
S. van der Werf

²The Netherlands Fatigue Research Group Nijmegen, Department of Medical Psychology and Internal Medicine, University Hospital Nijmegen, Nijmegen, The Netherlands
J. Prins

²The Netherlands Fatigue Research Group Nijmegen, Department of Medical Psychology and Internal Medicine, University Hospital Nijmegen, Nijmegen, The Netherlands
L. A. N. Amaral

³Department of Chemical Engineering, Northwestern University, Evanston, IL, USA
B. H. Natelson

⁴Department of Neurosciences, New Jersey Medical School, East Orange, NJ, USA
Y. Yamamoto

¹Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, Japan

⁴Department of Neurosciences, New Jersey Medical School, East Orange, NJ, USA

⁵PRESTO, Japan Science and Technology Corporation, Saitama, Japan

Abstract

Summary

Objectives: Our objectives were to study the temporal correlation of physical activity time series in patients with chronic fatigue syndrome (CFS) during normal daily life and to examine if it could identify the altered physical activity in these patients.

Methods: Fractal scaling exponents of diurnal and nocturnal physical activity time series in 10 CFS patients and 6 healthy control subjects (CON) were calculated by the detrended fluctuation analysis (DFA) and the wavelet transform modulus maxima (WTMM) method. We hypo-thesized that, due to their illness- and/or fatigue-induced resting episodes, altered physical activity patterns in CFS patients might be observed at the interruption of activity bursts. Thus, we further developed a new method, the wavelet transform negative modulus maxima (WTNMM) method, which could evaluate the temporal correlation at the interruption of activities. We compared the fractal scaling exponents for CFS and CON by each method.

Results: Both for CFS and CON, we found the fractal time structures in their diurnal physical activity records for at least up to 35 minutes. No group difference was found in nocturnal activities. The WTNMM method revealed that, in diurnal activities, CFS patients had significantly (p <0.01) smaller fractal scaling exponent (0.87 ± 0.03) compared to controls (1.01 ± 0.03). Such a difference was identified neither by the DFA nor WTMM method.

Conclusions: CFS patients had more abrupt interruptions of voluntary physical activity during diurnal periods in normal daily life, probed by the decreased correlation in the negative modulus maxima of the wavelet-transformed activity data, possibly due to their exaggerated fatigue.

Keywords

Chronic fatigue syndrome - physical activity - detrended fluctuation analysis - wavelet transform modulus maxima method

Full Text

References

References
1 Teicher MH. Actigraphy and motion analysis: New tools for psychiatry. Harvard Rev Psychiatry 1995; 3: 18-35.
2 van Hilten JJ, Kabel JF, Middelkoop HA, Kramer CG, Kerkhof GA, Roos RA. Assessment of response fluctuations in Parkinson’s disease by ambulatory wrist activity monitoring. Acta Neurol Scand 1993; 87 (03) 171-7.
3 Sisto SA, Tapp WN, LaManca JJ. et al. Physical activity before and after exercise in women with chronic fatigue syndrome. Q J Med 1998; 91: 465-73.
4 van der Werf SP, Prins JB, Vercoulen JH, van der Meer JW, Bleijenberg G. Identifying physical activity patterns in chronic fatigue syndrome using actigraphic assessment. J Psychosom Res 2000; 49: 373-9.
5 Selz KA, Mandell AJ, Anderson CM, Smotherman WP, Teicher MH. Distribution of local Mandelbrot-Hurst exponents: motor activity in in fetal rats of cocainized mothers and manic depressives. Fractals 1995; 3: 956-67.
6 Aoyagi N, Ohashi K, Tomono S, Yamamoto Y. Temporal contribution of body movement to very long-term heart rate variability in humans. Am J Physiol Heart Circ Physiol 2000; 278: H1035-41.
7 Amaral LA, Soares DJB, Luciano RS. et al. Power-law temporal auto-correlations in day-long records of human physical activity and their alterations with disease. Phys Rev E; submitted. 2002
8 Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Phys Rev E 1994; 49: 1685-9.
9 Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 1995; 5 (01) 82-7.
10 Muzy JF, Bacry E, Arneodo A. The multifractal formalism revisited with wavelets. Int J Bifurcat Chaos 1994; 4 (02) 245-302.
11 Fukuda K, Straus SE, Hickie I, Sharpe MC, Dobbins JG, Komaroff A. International Chronic Fatigue Syndrome Study Group. The chronic fatigue syndrome: A comprehensive approach to its definition and study. Ann Int Med 1992; 121: 953-69.
12 Ashkenazy Y, Ivanov PC, Havlin S, Peng CK, Goldberger AL, Stanley HE. Magnitude and sign correlations in heartbeat fluctuations. Phys Rev Lett 2001; 86 (09) 1900-3.
13 Hu K, Ivanov PC, Chen Z, Carpena P, Stanley HE. Effect of trends on detrended fluctuation analysis. Phys Rev E 2001; 64: 011114
14 Natelson BH. Facing and Fighting Fatigue. New Haven and London: Yale University Press; 1998