Abstract
Recurrence quantification analysis and multifractal analysis were used to study the encephalograms time series of the principal components of children with epilepsy. It is shown that epileptic seizures are accompanied by an increase in the determinism of the brain’s electrical activity process. This increase is due to the synchronization of neuronal activity during epileptic seizures. It is noted that this behavior is similar to the behavior of nonlinear systems of a different physical nature in catastrophic situations.
Similar content being viewed by others
REFERENCES
N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics (Nauka, Moscow, 1981).
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge Univ. Press, 1995).
G. G. Malinetskii and A. B. Potapov, Current Problems of Nonlinear Dynamics (Editorial URSS, Moscow, 2000).
C. C. Olson, J. M. Nichols, and L. N. Virgin, Nonlinear Dyn. 70, 381 (2012). https://doi.org/10.1007/s11071-012-0461-8
R. Hegger, H. Kantz, and T. Schreiber, Chaos 9, 413 (1999). https://doi.org/10.1063/1.166424
J. M. Nichols, S. T. Trickey, and M. Seaver, Mech. Syst. Signal Process. 20, 421 (2006). https://doi.org/10.1016/j.ymssp.2004.08.007
J. M. Nichols, M. Seavera, and S. T. Trickeya, J. Sound Vib. 297, 1 (2006). https://doi.org/10.1016/j.jsv.2006.01.025
V. L. Hilarov, Phys. Solid State 57, 2271 (2015). https://doi.org/10.1134/S1063783415110116
V. B. Smirnov, A. V. Ponomarev, and A. D. Zavyalov, Fiz. Zemli, No. 1, 38 (1995).
S. Kacimi and S. Laurens, J. Appl. Phys. 106, 024909 (2009). https://doi.org/10.1063/1.3169601
N. V. Zolotova and D. I. Ponyavin, Uch. Zap. S.-Peterb. Gos. Univ. Vopr. Geofiz., No. 38, 203 (2005).
V. S. Zakharov, Nelineinyi Mir 8, 234 (2010).
A. A. Lyubushin, J. Seismol. 19, 329 (2015). https://doi.org/10.1007/s10950-014-9468-6
V. B. Smirnov, A. V. Ponomarev, Q. Jiadong, and A. S. Cherepantsev, Izv., Phys. Solid Earth 41, 428 (2005).
X. L. Lei, O. Nishizawa, and K. Kusunose, Geophys. J. Int. 115, 79 (1993). https://doi.org/10.1111/j.1365-246X.1993.tb05589.x
P. V. Makarov and M. O. Eremin, Phys. Mesomech. 21, 283 (2018).
A. A. Mekler, Vestn. Nov. Med. Tekhnol. 14, 73 (2007).
A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. Ch. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C.-K. Peng, and H. E. Stanley, Circulation 101, E215 (2000). https://doi.org/10.1161/01.CIR.101.23.e215
A. Fabretti and M. Ausloos, Int. J. Mod. Phys. C 16, 671 (2005). https://doi.org/10.1142/S0129183105007492
Modelling and Forecasting Financial Data, Ed. by A. S. Soofi and C. Liangyue (Springer, 2002).
Nonlinear Economic Dynamics and Financial Modelling, Ed. by R. Dieci, X.-Z. He, and C. Hommes (Springer, 2014).
M. Faggini, Chaos 24, 042101 (2014). https://doi.org/10.1063/1.4903797
D. L. Turcotte, Rep. Prog. Phys. 62, 1377 (1999). https://doi.org/10.1088/0034-4885/62/10/201
J.-P. Eckmann, S. O. Kampost, and D. Ruelle, Europhys. Lett. 4, 973 (1987).
N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, Phys. Rep. 438, 237 (2007). https://doi.org/10.1016/j.physrep.2006.11.001
E. Feder, Fractals (Plenum, New York, 1988).
A. N. Pavlov and V. S. Anishchenko, Phys.-Usp. 50, 819 (2007).
F. Sharbrough, G.-E. Chatrian, R. P. Lesser, H. Luders, M. Nuwer, and T. W. Picton, J. Clin. Neurophysiol. 8, 200 (1991).
K. H. Esbensen, Multivariate Data Analysis—InPractice (Camo, 2000).
V. P. D’yakonov, Wavelets. From Theory to Practice (SOLON-Press, Moscow, 2010).
A. Kharbouch, A. Shoeb, and J. Guttag, Epilepsy Behav. 22, S29 (2011). https://doi.org/10.1016/j.yebeh.2011.08.031
L. R. Zenkov, Clinical Electroencephalography (with Elements of Epileptology). Guidelines for Physicians (MEDpressinform, Moscow, 2017).
A. Shoeb, PhD Thesis (Massachusetts Inst. of Technology, 2009).
H. Wendt, P. Abry, and S. Jaffard, IEEE Signal Process. Mag. 24 (4), 38 (2007). https://doi.org/10.1109/MSP.2007.4286563
H. Wendt, S. G. Roux, S. Jaffard, and P. Abry, Signal Process. 89, 1100 (2009). https://doi.org/10.1016/j.sigpro.2008.12.015
J. F. Muzy, E. Bacry, and A. Arneodo, Phys. Rev. E 47, 875 (1993). https://doi.org/10.1103/PhysRevE.47.875
P. Ch. Ivanov, N. L. A. Amaral, A. L. Goldberger, S. Havlin, M. G. Rosenblum, Z. R. Struzikk, and H. E. Stanley, Nature 399, 461 (1999). https://doi.org/10.1038/20924
D. Makowiec, R. Galaska, A. Dudkowska, A. Rynkiewicz, and M. Zwierz, Phys. A 369, 632 (2006). https://doi.org/10.1016/j.physa.2006.02.038
V. L. Hilarov, V. E. Korsukov, P. N. Butenko, and V. N. Svetlov, Phys. Solid State 46, 1868 (2004).
V. E. Korsukov, S. A. Knyazev, P. N. Butenko, V. L. Gilyarov, M. M. Korsukova, I. A. Nyapshaev, and B. A. Obidov, Phys. Solid State 59, 316 (2017). https://doi.org/10.1134/S1063783417020135
S. J. Gibowicz and S. Lasocki, in Advances in Geophysics, Ed. by R. Dmowska and B. Saltzman (Elsevier, 2001), Vol. 44, p. 39. https://doi.org/10.1016/S0065-2687(00)80007-2
V. A. Kasimova, G. N. Kopylova, and A. A. Lyubushin, Izv., Phys. Solid Earth 54, 269 (2018). https://doi.org/10.1134/S1069351318020076
V. L. Gilyarov, E. E. Damaskinskaya, and I. Yu. Rasskazov, Probl. Nedropol’zovaniya, No. 2, 53 (2016). https://doi.org/10.18454/2313-1586.2016.02.05
E. E. Damaskinskaya, V. L. Hilarov, I. A. Panteleev, D. R. Gafurova, and D. I. Frolov, Phys. Solid State 60, 1821 (2018). https://doi.org/10.1134/S106378341809007X
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he does not have any conflicts of interest.
Additional information
Translated by M. Batrukova
Rights and permissions
About this article
Cite this article
Hilarov, V.L. Identification of Dynamic Patterns of Epileptic Seizures in Children by Nonlinear Mechanics Methods. Tech. Phys. 65, 485–491 (2020). https://doi.org/10.1134/S106378422003007X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106378422003007X