Effect of Spinal Cord Injury on Nonlinear Complexity of Skin Blood Flow Oscillations

  • Yih-Kuen Jan
  • Fuyuan Liao
  • Stephanie Burns
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6768)


This study investigated the effect of spinal cord injury (SCI) on nonlinear complexity of skin blood flow oscillations (BFO). Complexity of the characteristic frequencies embedded in BFO was described by the scaling coefficient derived by detrended fluctuation analysis (DFA) and the range of scaling coefficients derived from multifractal detrended fluctuation analysis (MDFA) in specific scale intervals. 23 subjects were recruited into this study, including 11 people with SCI and 12 healthy controls. Local heating-induced maximal sacral skin blood flow was measured by laser Doppler flowmetry. The results showed that metabolic BFO (0.0095-0.02 Hz) exhibited significantly lower complexity in people with SCI as compared with healthy controls (p<0.01) during maximal vasodilation. This study demonstrated that complexity analysis of BFO can provide information of blood flow dynamics beyond traditional spectral analysis.


blood flow oscillations complexity detrended fluctuation analysis multifractal detrended fluctuation analysis spinal cord injury 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alexander, M.S., Biering-Sorensen, F., Bodner, D., Brackett, N.L., Cardenas, D., Charlifue, S., et al.: International standards to document remaining autonomic function after spinal cord injury. Spinal Cord 47(1), 36–43 (2009)CrossRefGoogle Scholar
  2. 2.
    Nixon, J., Cranny, G., Bond, S.: Pathology, diagnosis, and classification of pressure ulcers: comparing clinical and imaging techniques. Wound Repair Regen 13(4), 365–372 (2005)CrossRefGoogle Scholar
  3. 3.
    Stefanovska, A., Bracic, M., Kvernmo, H.D.: Wavelet analysis of oscillations in the peripheral blood circulation measured by laser Doppler technique. IEEE Trans. Biomed. Eng. 46(10), 1230–1239 (1999)CrossRefGoogle Scholar
  4. 4.
    Bracic, M., Stefanovska, A.: Wavelet-based analysis of human blood-flow dynamics. Bull. Math. Biol. 60(5), 919–935 (1998)CrossRefMATHGoogle Scholar
  5. 5.
    Stefanovska, A., Bracic, M.: Physics of the human cardiovascular system. Contemporary Physics 40(1), 31–55 (1999)CrossRefGoogle Scholar
  6. 6.
    Goldberger, A.L., Peng, C.K., Lipsitz, L.A.: What is physiologic complexity and how does it change with aging and disease? Neurobiology of Aging 23(1), 23–26 (2002)CrossRefGoogle Scholar
  7. 7.
    Lipsitz, L.A., Goldberger, A.L.: Loss of Complexity and Aging - Potential Applications of Fractals and Chaos Theory to Senescence. Jama-Journal of the American Medical Association 267(13), 1806–1809 (1992)CrossRefGoogle Scholar
  8. 8.
    Goldberger, A.L., Amaral, L.A.N., Hausdorff, J.M., Ivanov, P.C., Peng, C.K., Stanley, H.E.: Fractal dynamics in physiology: Alterations with disease and aging. Proceedings of the National Academy of Sciences of the United States of America 99, 2466–2472 (2002)CrossRefGoogle Scholar
  9. 9.
    Goldberger, A.: Complexity loss, aging, and disease: Is there a dynamical “Theory of Everything Pathologic?”. Journal of Critical Care 25(3), E2 (2010)CrossRefGoogle Scholar
  10. 10.
    Ivanov, P.C., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z.R., et al.: Multifractality in human heartbeat dynamics. Nature 399(6735), 461–465 (1999)CrossRefGoogle Scholar
  11. 11.
    Merati, G., Di Rienzo, M., Parati, G., Veicsteinas, A., Castiglioni, P.: Assessment of the autonomic control of heart rate variability in healthy and spinal-cord injured subjects: contribution of different complexity-based estimators. IEEE Trans. Biomed. Eng. 53(1), 43–52 (2006)CrossRefGoogle Scholar
  12. 12.
    Harbourne, R.T., Stergiou, N.: Movement Variability and the Use of Nonlinear Tools: Principles to Guide Physical Therapist Practice Response. Physical Therapy 89(3), 284–285 (2009)CrossRefGoogle Scholar
  13. 13.
    Esen, F., Esen, H.: Detrended fluctuation analysis of laser Doppler flowmetry time series: the effect of extrinsic and intrinsic factors on the fractal scaling of microvascular blood flow. Physiological Measurement 27(11), 1241–1253 (2006)CrossRefGoogle Scholar
  14. 14.
    Liao, F., Garrison, D.W., Jan, Y.K.: Relationship between nonlinear properties of sacral skin blood flow oscillations and vasodilatory function in people at risk for pressure ulcers. Microvasc Res. 80(1), 44–53 (2010)CrossRefGoogle Scholar
  15. 15.
    Geyer, M.J., Jan, Y.K., Brienza, D.M., Boninger, M.L.: Using wavelet analysis to characterize the thermoregulatory mechanisms of sacral skin blood flow. Journal of Rehabilitation Research and Development 41(6A), 797–805 (2004)CrossRefGoogle Scholar
  16. 16.
    Jan, Y.K., Brienza, D.M., Geyer, M.J.: Analysis of week-to-week variability in skin blood flow measurements using wavelet transforms. Clin. Physiol. Funct. Imaging 25(5), 253–262 (2005)CrossRefGoogle Scholar
  17. 17.
    Jan, Y.K., Brienza, D.M., Geyer, M.J., Karg, P.: Wavelet-based spectrum analysis of sacral skin blood flow response to alternating pressure. Arch. Phys. Med. Rehabil. 89(1), 137–145 (2008)CrossRefGoogle Scholar
  18. 18.
    Jan, Y.K., Struck, B.D., Foreman, R.D., Robinson, C.: Wavelet analysis of sacral skin blood flow oscillations to assess soft tissue viability in older adults. Microvasc. Res. 78(2), 162–168 (2009)CrossRefGoogle Scholar
  19. 19.
    Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: Mosaic Organization of DNA Nucleotides. Physical Review E 49(2), 1685–1689 (1994)CrossRefGoogle Scholar
  20. 20.
    Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Physica a-Statistical Mechanics and Its Applications 316(1-4), 87–114 (2002)CrossRefMATHGoogle Scholar
  21. 21.
    Minson, C.T., Berry, L.T., Joyner, M.J.: Nitric oxide and neurally mediated regulation of skin blood flow during local heating. Journal of Applied Physiology 91(4), 1619–1626 (2001)Google Scholar
  22. 22.
    Peng, C.K., Havlin, S., Hausdorff, J.M., Mietus, J.E., Stanley, H.E., Goldberger, A.L.: Fractal mechanisms and heart rate dynamics - Long-range correlations and their breakdown with disease. Journal of Electrocardiology 28, 59–65 (1995)CrossRefGoogle Scholar
  23. 23.
    Meyer, M., Stiedl, O.: Self-affine fractal variability of human heartbeat interval dynamics in health and disease. Eur. J. Appl. Physiol. 90(3-4), 305–316 (2003)CrossRefGoogle Scholar
  24. 24.
    Chen, Z., Ivanov, P., Hu, K., Stanley, H.E.: Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 65(4 Pt 1), 041107 (2002)CrossRefGoogle Scholar
  25. 25.
    Hu, K., Ivanov, P.C., Chen, Z., Carpena, P., Stanley, H.E.: Effect of trends on detrended fluctuation analysis. Physical Review E 6401(1) (2001)Google Scholar
  26. 26.
    Havlin, S., Amaral, L.A., Ashkenazy, Y., Goldberger, A.L., Ivanov, P., Peng, C.K., et al.: Application of statistical physics to heartbeat diagnosis. Physica a-Statistical Mechanics and Its Applications 274(1-2), 99–110 (1999)CrossRefGoogle Scholar
  27. 27.
    Humeau, A., Chapeau-Blondeau, F., Rousseau, D., Rousseau, P., Trzepizur, W., Abraham, P.: Multifractality, sample entropy, and wavelet analyses for age-related changes in the peripheral cardiovascular system: Preliminary results. Medical Physics 35(2), 717–723 (2008)CrossRefGoogle Scholar
  28. 28.
    Humeau, A., Chapeau-Blondeau, F., Rousseau, D., Tartas, M., Fromy, B., Abraham, P.: Multifractality in the peripheral cardiovascular system from pointwise holder exponents of laser Doppler flowmetry signals. Biophysical Journal 93(12), L59–L61 (2007)CrossRefGoogle Scholar
  29. 29.
    Arneodo, A., Bacry, E., Muzy, J.F.: The Thermodynamics of Fractals Revisited with Wavelets. Physica a-Statistical Mechanics and Its Applications 213(1-2), 232–275 (1995)CrossRefMATHGoogle Scholar
  30. 30.
    Bacry, E., Muzy, J.F., Arneodo, A.: Singularity Spectrum of Fractal Signals from Wavelet Analysis - Exact Results. Journal of Statistical Physics 70(3-4), 635–674 (1993)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Oswiecimka, P., Kwapien, J., Drozdz, S.: Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 74(1 Pt 2), 016103 (2006)CrossRefGoogle Scholar
  32. 32.
    Heneghan, C., McDarby, G.: Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Physical Review E 62(5), 6103–6110 (2000)CrossRefGoogle Scholar
  33. 33.
    Willson, K., Francis, D.P., Wensel, R., Coats, A.J.S., Parker, K.H.: Relationship between detrended fluctuation analysis and spectral analysis of heart-rate variability. Physiological Measurement 23(2), 385–401 (2002)CrossRefGoogle Scholar
  34. 34.
    Li, Z., Leung, J.Y., Tam, E.W., Mak, A.F.: Wavelet analysis of skin blood oscillations in persons with spinal cord injury and able-bodied subjects. Arch. Phys. Med. Rehabil. 87(9), 1207–1212 (2006), quiz 1287 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yih-Kuen Jan
    • 1
  • Fuyuan Liao
    • 1
  • Stephanie Burns
    • 2
  1. 1.University of Oklahoma Health Sciences Center, Department of Rehabilitation SciencesOklahoma CityUSA
  2. 2.Oklahoma City Veterans Affairs Medical Center, Department of Neurology and RehabilitationOklahoma CityUSA

Personalised recommendations