DOI: https://doi.org/10.31071/kit2014.11.01

Inventory reference

ISSN 1812-7231 Klin.inform.telemed. Volume 10, Issue 11, 2014, Pages 10–20

Author(s)

O. Yu. Mayorov^{1, 2, 3}, V. N. Fenchenko^{1, 2, 4}

Institution(s)

¹Institute for Medical Informatics and Telemedicine LTD, Kharkiv, Ukraine ²Kharkiv Medical Academy of Postgraduate Education, Ministry of Healthcare of Ukraine ³Institute of Children and Adolescents Health protection NAMS of Ukraine, Kharkiv ⁴B. Verkin Physical-technical Institute of Low Temperature NAS of Ukraine, Kharkiv

Article title

Calculation of the correlation dimension and entropy of EEG signals in cluster computing systems

Abstract (resume)

Introduction. During the study of the multifractals of bioelectrical brain (EEG, ERP) and heart (ECG, Heart Rate Variability) signals, the correct calculation of correlation dimensions D₂ is essential.

Formulation of the problem. Methodology. In order to avoid system errors, the segment of the EEG signal should be stationary and extensive. According to the Tsonis criteria (A. Tsonis), the duration of EEG series with D₂=4±8 is equal to (1±2)10⁵ counts. It is a time consuming process which requires powerful computing systems. However, unified criteria which are necessary for the selection of the following parameters: 1) offset amount (delay) d for the attractor reconstruction, 2) estimation of the required dimensionality of the reconstruction area m, 3) selection of the minimal size of cells ε, 4) number of points K for the calculation of the D₂ value limits, are missing. Subjective selection of the parameters excludes the opportunity of cluster systems application, makes difficult the comparison of results obtained by different researches.

The object of the study is to design methods of computerization of correlation dimensions D₂ and correlation entropy H₂, for using cluster computing systems without operator's participation for subjective selection of computation parameters.

Study results. The attractor reconstruction based on cluster systems with different d values for choosing of the optimal offset amount (delay) d has been proposed. The modification of the Theiler computational procedure (Theiler J.) which helps to avoid errors caused by the insufficient length of the biological signals has been developed. In this case, too closely located points are not taken into account for the summation, and Gauss nucleus (J. C. Gauss) is used instead of Heaviside function (O. Heaviside). The algorithm of automatic search of correlation dimension values D₂(m) and correlation entropy H₂ on the Rapp (P. Rapp) plot's plateau have been proposed.

Conclusion. Automatic computation of the correlation dimension D₂(m) and correlation entropy H₂ of biological signals allows to use the cluster system, reduces labor intensiveness, removes subjective factor in selecting of attractor reconstruction parameters, and allows to obtain comparable results in different laboratories.

Keywords

EEG, Bioelectrical activity, Deterministic chaos, Reconstruction, Entropy, Dimension, Cluster computing systems

References

1. Adeli H., Ghosh-Dastidar and Dadmehr N. Automated EEG-based diagnosis of neurological disorders. Inventing the Future of Neurology. In corroboration with Nahid Dadmehr, M. D. CRC Press, Taylor & Francis Group, 2010, 387 p.

2. Advanced Biosignal Processing. Advances in Neuroelectric and Neuromagnetic Methods. Ed. by Nait-Ali A. Springer-Verlag, Berlin Heidelberg, 2009, 378 p.

3. Azulay D.-O. D., Renoux B. and Ivarsson M. Evidence of a pharmacodynamic EEG profile in rats following clonidine administration using a nonlinear analysis. Nonlinear Biomedical Physics, 2011, vol. 5, iss. 4. doi: 10.1186/1753-4631-5-4
https://doi.org/10.1186/1753-4631-5-4

4. Babloyantz A. and Destexhe A. Low Dimensional Chaos in an Instance of Epilepsy. Proc. Natl. Acad. Sci. USA, 1986, vol. 83, pp. 3513–3517.
https://doi.org/10.1073/pnas.83.10.3513
PMid:3085091
PMCid:PMC323547

5. Brain Signal Analysis: Advances in Neuroelectric and Neuromagnetic Methods. Ed. by T. C. Handy. Massachusetts Institute of Technology, 2009, 247 p.
https://doi.org/10.7551/mitpress/9780262013086.001.0001

6. Cappe C., Thelen A., Romei V., Thut G., and Murray M. M. Looming Signals Reveal Synergistic Principles of Multisensory Integration. The Journal of Neuroscience, 2012, vol. 32, iss. 4, pp. 1171–1182.
https://doi.org/10.1523/JNEUROSCI.5517-11.2012
PMid:22279203

7. Faure P. & Korn H. Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation. Les Comptes rendus de l'Acad'emie des sciences III, 2001, vol. 32, iss. 4, iss. 9, pp. 773–793.

8. Fernбndez A., Mйndez M. A., Hornero R., Ortiz T., Lуpez-Ibor J. J. Analysis of brain complexity and mental disorders. Actas Esp Psiquiatr, 2010, vol. 38, iss. 4, pp. 229-238.

9. Freeman W. J. Tutorial on neurobiology: From single neurons to brain chaos. Int. J. Bifurc. Chaos, 1992, vol. 12, pp. 451–482.
https://doi.org/10.1142/S0218127492000653

10. Galka A. Topics in Nonlinear Time Series Analysis — With Implications for EEG Analysis. Advanced Series in Nonlinear Dynamics. Ed. by R. S. MacKay, World Scientific Publ. Company, Singapore, 2000, vol. 14, 342 p.
https://doi.org/10.1142/4286

11. Ghosh-Dastidar S., Adeli H., and Dadmehr N. Mixed-Band Wavelet-Chaos-Neural Network Methodology for Epilepsy and Epileptic Seizure Detection. IEEE Trans. on Biomed. Eng., 2007, vol. 54, iss. 9, pp. 1545–1551.
https://doi.org/10.1109/TBME.2007.891945
PMid:17867346

12. Goldberger A. L. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet, 1996, iss. 347, pp. 1312–1314.
https://doi.org/10.1016/S0140-6736(96)90948-4

13. Grassberger P., Procaccia I. Characterization of strange attractors. Phys. Rev. Lett., 1983, vol. 50, iss. 5, pp. 346–349.
https://doi.org/10.1103/PhysRevLett.50.346

14. Harikrishnan K. P., Misra R., Ambika G. & Kembhavi A. K. A non subjective approach to the GP algorithm for analyzing noisy time series. Physica D: Nonlinear Phenomena, 2006, vol. 215, iss. 2, pp. 137–145.
https://doi.org/10.1016/j.physd.2006.01.027

15. Hegger R., Kantz H. and Schreiber Th. Practical Implementation of Nonlinear Time Series Methods: The TISEAN package. CHAOS, 1999, vol. 9, iss. 2. pp. 413-435.
https://doi.org/10.1063/1.166424
PMid:12779839

16. Hively L. M., Protopopescu V. A. Channel-consistent forewarning of epileptic events from scalp EEG. IEEE Transactions on Biomedical Engineering, 2003, vol. 50, iss. 5, pp. 584–593.
https://doi.org/10.1109/TBME.2003.810693
PMid:12769434

17. Ivanov P. Ch., Amaral L. A. N., Goldberger A. L. & Stanley H. E. Stochastic feedback and the eregulation of biological rhythms. Europhys. Lett., 1998, vol. 43, iss. 4, pp. 363–368.
https://doi.org/10.1209/epl/i1998-00366-3
PMid:11542723

18. Ivanov P. Ch., Amaral L. A. N., Goldberger A. L., Havlin Sh., Rosenblum M. G., Struzik Z. R. & Stanley H. E. Multifractality in human heartbeat dynamics. Nature, 1999, vol. 399, iss. 3, pp. 461–465.
https://doi.org/10.1038/20924
PMid:10365957

19. Jelles B., Scheltens Ph., van der Flier W. M., Jonkman E. J., Lopes da Silva F. H., Stam C. J. Global dynamical analysis of the EEG in Alzheimer's disease: Frequency-specific changes of functional interactions. J. Clinical Neurophysiology, 2008, vol. 119, pp. 837–841.
https://doi.org/10.1016/j.clinph.2007.12.002
PMid:18258479

20. Jeong J., Chae J.-H., Kim S. Y., Han S.-H. Nonlinear dynamic analysis of the EEG in patients with Alzheimer's disease and vascular dementia. J. Clinical Neurophysiology, 2001, vol. 18, iss. 1. pp. 58–67.
https://doi.org/10.1097/00004691-200101000-00010
PMid:11290940

21. Kannathal N., Lim C. M., Rajendra A. U., Sadasivan P. K. Entropies for detection of epilepsy in EEG. Computer methods and programs in biomedicine, 2005, vol. 80, iss. 3, pp. 187–194.
https://doi.org/10.1016/j.cmpb.2005.06.012
PMid:16219385

22. Korn H., & Faure P. Is there chaos in the brain? II. Experimental evidence and related models. Comptes rendus biologies, 2003, vol. 326, iss. 9, pp. 787–840.
https://doi.org/10.1016/j.crvi.2003.09.011
PMid:14694754

23. Li X. Temporal structure of neuronal population oscillations with empirical model decomposition. Phys. Lett. A., 2006, vol. 356. pp. 237–241.
https://doi.org/10.1016/j.physleta.2006.03.045

24. Li Y., Tong S., Liu D., Gai Y., Wang X., Wang J., Qiu Y., Zhu Y. Abnormal EEG complexity in patients with schizophrenia and depression. J. Clinical Neurophysiology, 2008, vol. 119, iss. 6, pp. 1232–1241.
https://doi.org/10.1016/j.clinph.2008.01.104
PMid:18396454

25. Lopes da Silva F. H. The Impact of EEG/MEG Signal Processing and Modeling in the Diagnostic and Management of Epilepsy. IEEE Reviews in Biomedical Engineering, 2008, vol. 1, pp. 143-156.
https://doi.org/10.1109/RBME.2008.2008246
PMid:22274902

26. Mayorov O. Yu., Fritzsche M., Glukhov A. B., and oth. New neurodiagnostics technology for brain research on the basis of multivariate and nonlinear (deterministic chaos) analysis of EEG. In Proc. of the 2-nd Euro. Congr. "Achievements in space medicine into health care practice and industry". Pabst Science Publ., 2003. pp.157-166.

27. Palus M. Nonlinearity in normal human EEG: Cycles, temporal asymmetry, nonstationarity and randomness, not chaos. Biological Cybernetics, 1996, vol. 75, iss. 5, pp. 389–396.
PMid:8983161

28. Pereda E., Quiroga R. Q., Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals. Progress in Neurobiology, 2005, vol. 77, pp. 1–37.
https://doi.org/10.1016/j.pneurobio.2005.10.003
PMid:16289760

29. Pritchard W. S., Krieble K. K., and Duke D. W. On the validity of estimating EEG correlation dimension from a spatial embedding. Psychophysiology, 1996, vol. 33, iss. 4, pp. 362–368.
https://doi.org/10.1111/j.1469-8986.1996.tb01060.x
PMid:8753935

30. Quantitative EEG Analysis Methods and Clinical Applications. Ed. by S. Tong, Thakor N. V., Artech House, 2009, 421 p.

31. Rényi A. On measures of information and entropy. Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 1960, 1961, pp. 547–561.

32. Schiff S. J., Jerger K., Duong D. H., Chang T., Spano M. L. and Ditto W. L. Controlling chaos in the brain. Nature, 1994. vol. 370, iss. 6491, pp. 615–620.
https://doi.org/10.1038/370615a0
PMid:8065447

33. Sohn H., Kim I., Lee W., Peterson B. S., Hong H., Chae J.-H., Hong S., Jeong J. Linear and non-linear EEG analysis of adolescents with attention-deficit/hyperactivity disorder during a cognitive task. J. Clinical Neurophysiology, 2010, vol. 121, iss. 11, pp. 1863-1870.
https://doi.org/10.1016/j.clinph.2010.04.007

34. Sprott J. C., Rowlands G. Chaos data analyzer, the professional version. AIP, NY, 1995.

35. Harikrishnan K. P., Misra R., Ambika G., Kembhavi A. K. A non subjective approach to the GP algorithm for analyzing noisy time series. Physica D: Nonlinear Phenomena, 2006, vol. 215, iss. 2. pp. 137–145.
https://doi.org/10.1016/j.physd.2006.01.027

36. Takens F. Detecting strange attractors in turbulence. Dynamical Systems and Turbulence. Under edit D. A. Rand and L. S. Young. Warwick 1980, Lecture Notes in Mathematics, Springer, Berlin, 1981, vol. 898, pp. 366–381.
https://doi.org/10.1007/BFb0091924

37. Theiler J. On the evidence for low-dimensional chaos in an epileptic electroencephalogram. Phys. Lett. A., 1995, vol. 196, pp. 335–341.
https://doi.org/10.1016/0375-9601(94)00856-K

38. Theiler J. Spurious dimension from correlation algorithms applied to limited time-series data. Physical Review, 1986, A. 34, iss.3, p. 2427.

39. Tsakalis K., and Iasemidis L. D., Control Aspects of a Theoretical Model for Epileptic Seizures. Int. J. Bifurcations Chaos, 2006, vol. 16, pp. 2013–2027.
https://doi.org/10.1142/S0218127406015866

40. Tsonis A. Chaos: from Theory to Applications. NY. Premium Press, 1992.
https://doi.org/10.1007/978-1-4615-3360-3

41. Bozhokin S. V., Parshin D. A. Fraktaly i multifraktaly [Fractals and multifractals}. Izhevsk, NITs Regulyarnayay i haoticheskayay dinamika [Regular and Chaotic Dynamics], 2001, 128 p. (In Russ.).

42. Gudkov G. V., Penzhoyan G. A., Turichenko O. V. Multifractal nature of fetal heart rate during its various functional states. Vestnik novyh meditsinskih tehnologiy [Herald of new medical technologies], 2006, vol. 13, iss. 3, pp. 101–104. (In Russ.).
PMCid:PMC1356114

43. Koychubekov B. K., Sorokina M. A., Pashev V. I. [EEG features of nonlinear dynamics in different age groups]. Intern. J. of Experimental Education, 2013, iss. 4, pp. 68–72. (In Russ.)

44. Krownover R. M. Introduction to Fractals and Chaos. Jones and Bartlett Publ., 1999, 352 p.

45. Mayorov O. Yu., Glukchov A. B., Fenchenko V. N., Prognimak A. B. Realization of the delay method with the help of an estimation of sizes of axes of an attractor restored in a phase space. Trudy Instituta kibernetiki NAN Ukrainy [Proc. of the Institute of Cybernetics of the NAS of Ukraine], 2007, iss. 153, pp. 3–11. (In Russ.).

46. Mayorov O. Yu., Fenchenko V. N. Increase reliability of bioelectric activity (EEG, ECG and HRV) deterministic chaos researches by the nonlinear analysis methods. Klinicheskaya informatika i Telemeditsina [Clinical informatics and Telemedicine], 2009, vol.5, iss. 6, pp. 10–17. (In Russ.).

47. Mayorov O. Yu., Fenchenko V. N. About revealing neurodynamic systems of the brain by methods of the multidimensional spectral analysis and deterministic chaos on EEG-signals. Trudy Instituta kibernetiki NAN Ukrainy [Proc. of the Institute of Cybernetics of the NAS of Ukraine], 2009, iss. 155, pp. 3–9. (In Russ.).

48. Malinetskii G. G., Potapov A. B. Sovremennye problemy nelineynoy dinamiki [Modern problems of nonlinear dynamics]. Moscow, URSS Publ, 2002, 360 p. (In Russ.).

49. Meckler A. A. Application of the device nonlinear dynamical systems analysis for EEG signal processing. Vestnik novyh meditsinskih tehnologiy [Herald of new medical technologies], 2007, vol. XIV, iss. 1, pp. 73–76. (In Russ.).

50. Schuster H. G. Deterministic Chaos: An Introduction, 2nd edn, Weinheim: Physik Verlag, 1988, 220 p.

51. Rapp P. E., Bashore T., Martinerie J., Albano A. Zimmerman I. and Mess A. Dynamics of Brain Electrical Activity. Brain topography, 1989, iss. 2, pp. 99–118.
https://doi.org/10.1007/BF01128848
PMid:2641481

Full-text version http://kit-journal.com.ua/en/viewer_en.html?doc/2014_11/4.pdf