ISSUE 181, article 6

DOI:https://doi.org/10.15407/kvt181.01.070

Kibern. vyčisl. teh., 2015, Issue 181, pp.

Mayorov O.Y.

Kharkiv Medical Academy of Postgraduate Education, Kharkiv, Ukraine

Fenchenko V.N.

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv

MULTIFRACTAL ANALYSIS IN THE STUDY OF BRAIN BIOELECTRIC ACTIVITY

Introduction. A summary electroencephalogram (EEG) is composed of superimposed slow waves. The EEG reflects sophisticated cortical-subcortical interactions and conceals activity of multiple neuronal systems; each of them is characterized by determined neurodynamics.
The purpose of work is to create a method of objective quantitative assessment of parameters of multifractal summary bioelectric activity (EEG); to study EEG multifractality in healthy volunteers, subjects in altered states of conscious and pathologic EEGs.
Results. For the qualitative estimation of the multifractality of the EEG signal, the use of multifractal spectrum width, which can serve as an indicator of altered and pathologic brain states, is proposed. The state of different brain areas can also be assessed according to the offset value of a singularity spectrum of the transposition between different states. Analysis of Hölder exponents can provide an exact diagnostic tool and allow substantial interpretation of different processes in the brain.

Keywords: EEG, summary brain bioelectric activity, multifractality, wavelet transform maximum modulus method, method of multifractal detrended fluctuation analysis, Hölder exponent.

Download full text (ru)!

References

1 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 (Lond.), 1999. vol. 399. pp. 461–465.

2 Arneodo A., D’Aubenton-Carafa Y., Audit B., Bacry E., Muzy J.F., Thermes C. What can we learn with wavelets about DNA sequences? Physica, 1998. vol. A 249. pp. 439–448.

3 Stanley H.E., Amaral L.A.N., Goldberger A.L., Havlin S., Ivanov P.Ch., Peng C.-K. Statistical physics and physiology: Monofractal and multifractal approaches. Physica A, 1999. vol. 270. pp. 309–324. https://doi.org/10.1016/S0378-4371(99)00230-7

4 Nunes A.LA., Ivanov P.C., 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., 2001, vol. 86, pp. 6026–6029. https://doi.org/10.1103/PhysRevLett.86.6026

5 Ivanov P.Ch., Nunes Amaral L.A., Goldberger A.L., Havlin Sh., Rosenblum M.G., Stanley H.E., Struzik Zbigniew R. From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos, 2001, vol. 11 pp. 641–652. https://doi.org/10.1063/1.1395631

6 Marrone A., Polosa A. D., Scioscia G., Stramaglia S. and Zenzola A. Multiscale analysis of blood pressure signals. Phys. Rev. E, 1999, vol. 60. pp. 1088–1091. https://doi.org/10.1103/PhysRevE.60.1088

7 Muzy J.F., Bacry E. and Arneodo A. Wavelets and multifractal formalism for singular signals: application to turbulence data. Phys. Rev. Lett., 1991. vol. 67, pp. 3515–3518. https://doi.org/10.1103/PhysRevLett.67.3515

8 Muzy J.F., Bacry E., Arneodo A. Phys. Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E, 1993, vol. 47, pp. 875–884. https://doi.org/10.1103/PhysRevE.47.875

9 Muzy J.F., Bacry E., Arneodo A. The multifractal formalism revisited with wavelets. Int.J. Bifurcation Chaos, 1994. vol. 4, no. 2. p. 245–302. https://doi.org/10.1142/S0218127494000204

10 Kantelhardt J.W., Zschiegner S.A., Bunde A., Havlin S., Koscielny-Bunde E., Stanley H.E. Multifractal detrended fluctuation analysis of non-stationary time series. Physica A, 2002, no. 316, pp. 87–114. https://doi.org/10.1016/S0378-4371(02)01383-3

11 Kantelhardt J.W., Koscielny-Bunde E., Rego H.H.A., Havlin S., Bunde A. Detecting long-range correlations with detrended fluctuation analysis. Physica A, 2001, no. 295, pp. 441–454.

12 Mandelbrot B.B. The Fractal Geometry of Nature. San Francisco: W.H. Freeman, 1982, 468p.

13 Pavlov A.P., Anischenko V.S. Multifractal analysis of complex signals. Successes of physical sciences, 2007, vol. 177, no. 8, pp. 859–876 (in Russian).

14 Grassberger P. Generalized dimensions of strange attractors. Physics Letters A, 1983, vol. 97, no. 6, pp. 227–230. https://doi.org/10.1016/0375-9601(83)90753-3

15 Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D, 1983, Nonlinear Phenomena, vol. 9, no. 1–2, pp. 189–208. https://doi.org/10.1016/0167-2789(83)90298-1

16 Hentschel H.G.E., Procaccia I. The infinite number of generalized dimensions of fractals and strange attractors. Physica D, 1983, Nonlinear Phenomena, vol. 8, no. 3, pp. 435–444. https://doi.org/10.1016/0167-2789(83)90235-X

17 Grassberger P., Procaccia I. Characterization of Strange Attractors. Physical Review Letters, 1983, vol. 50, no. 5, pp. 346–349. https://doi.org/10.1103/PhysRevLett.50.346

18 Oswiecimka P., Kwapin J., Drozdz S. Wavelet versus detrended fluctuation analysis of multifractal structures. Physical Review E, 2006, Statistical, Nonlinear, and Soft Matter Physics, vol. 74, pp. 161–203.

19 Veneziano D., Moglen G.E., Bras R.L. Multifractal analysis: pitfalls of standard procedures and alternatives. Phys. Rev, E. 1995, vol. 52, pp.1387–1398. https://doi.org/10.1103/PhysRevE.52.1387

20 Olemskoy A.I. Synergetics of complex systems: Phenomenology and statistical theory. M.: Krasandz Publ., 2009. 384 p. (in Russian).

21 Kirichenko L.O. Comparative multifractal time series analysis by methods of detrending fluctuation analysis and maxima of modulus the wavelet transform. All-Ukrainian interdep. scientific – technical proceedings of ASM and automation devices. Kh.: Publ. KhNURE, 2011, Vol. 157. pp. 66–77 (in Russian).

22 Frish U., Parisi G. On the singularity structure of fully developed turbulence. In: Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. Proc. of the Intern. School of Physics “Enrico Fermi”, Course 88, Eds by M. Gil, R. Benzi, G. Parisi. Proc. Amsterdam. North-Holland, 1985, pp. 84–88.

Received 27.03.2015