OALibJ  Vol.2 No.1 , January 2015
Analysis of EEG Dynamics in Epileptic Patients and Healthy Subjects Using Hilbert Transform Scatter Plots
Abstract: In this study, we investigated the electroencephalogram (EEG) dynamics in normal and epileptic subjects using three newly defined quantifiers adapted from nonlinear dynamics and Hilbert transform scatter plots (HTSPs): dispersion entropy (DispEntropy), dispersion complexity (Disp Comp), and forbidden count (FC), hypothesizing that analysis of electroencephalogram (EEG) signals using nonlinear and deterministic chaos theory may provide clinicians with information for medical diagnosis and assessment of the applied therapy. DispEntropy evaluates irregularity of the EEG time series. DispComp and FC quantify degree of variability of the time series. Receiver operating characteristic (ROC) analysis reveals that all the three quantifiers can discriminate between seizure and non-seizure states with very high accuracy. The application of such a technique is justified by ascertaining the presence of nonlinearity in the EEG time series through the use of surrogate test. The false positive rejection of the null hypothesis is eliminated by employing Welch window before the computation of the Fourier transform and randomizing the phases, in the generation of the surrogate data. Paired t-test revealed significant differences between the measures of the original time series and those of their respective surrogated time series, indicating the presence of deterministic chaos in the original EEG time series.
Cite this paper: Kamath, C. (2015) Analysis of EEG Dynamics in Epileptic Patients and Healthy Subjects Using Hilbert Transform Scatter Plots. Open Access Library Journal, 2, 1-14. doi: 10.4236/oalib.1100745.

[1]   Bethesda, M.D. (2004) Seizures and Epilepsy: Hope through Research. National Institute of Neurological Disorders and Stroke (NINDS), 2004. Goy/health and medical/pubs/seizures and epilepsy htr.htm, NINDS.

[2]   Logar, C., Walzl, B. and Lechner, H. (1994) Role of Long-Term EEG Monitoring in Diagnosis and Treatment of Epilepsy. European Neurology, 34, 29-32.

[3]   Adeli, H., Ghosh-Dastidar, S. and Dadmehr, N. (2007) A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Sub-Bands to Detect Seizure and Epilepsy. IEEE Transactions on Biomedical Engineering, 54, 205-211.

[4]   Iasemidis, L.D., Sackellares, J.C., Zaveri, H.P. and Williams, W.J. (1990) Phase Space Topography and the Lyapunov Exponent of the Electrocorticogram in Partial Seizures. Brain Topography, 2, 187-201.

[5]   Iasemidis, L.D. and Sackellares, J.C. (1990) Long Time Scale Spatio-Temporal Patterns of Entrainment in Preictalecog Data in Human Temporal Lobe Epilepsy. Epilepsia, 31, 621.

[6]   Iasemidis, L.D. (1991) On the Dynamics of the Human Brain in Temporal Lobe Epilepsy. Ph.D. Dissertation, University of Michigan.

[7]   Iasemidis, L.D. and Sackellares, J.C. (1991) The Evolution with Time of the Spatial Distribution of the Largest Lyapunov Exponent on the Human Epileptic Cortex. In: Duke, D. and Pritchard, W., Eds., Measuring Chaos in the Human Brain, World Scientific, Singapore, 49-82.

[8]   Iasemidis, L.D. and Sackellares, J.C. (1996) Chaos Theory and Epilepsy. The Neuroscientist, 2, 118-126.

[9]   Iasemidis, L.D., Principe, J.C. and Sackellares, J.C. Measurement and Quantification of Spatiotemporal Dynamics of Human Epileptogenic Seizures. In: Akay, M., Ed., Nonlinear Biomedicalsignal Processing, IEEE Press, in Press.

[10]   Sackellares, J.C., Iasemidis, L.D., Shiau, D.S., Gilmore, R.L. and Roper, S.N. (2000) Epilepsy—When Chaos Fails. In: Lehnertz, K., Arnhold, J., Grassberger, P. and Elger, C.E., Eds., Chaos in Brain? World Scientific, Singapore, 112-133.

[11]   Klonowski, W., Jernajczyk, W., Niedzielska, K., Rydz, A. and Stepien, R. (1999) Quantitative Measure of Complexity of EEG Signal Dynamics. Acta Neurobiologiae Experimentalis, 59, 315-321.

[12]   Theiler, J. and Rapp, P.E. (1996) Re-Examination of the Evidence for Low-Dimensional, Nonlinear Structure in the Human Electroencephalogram. Electroencephalography and Clinical Neurophysiology, 98, 213-222.

[13]   Jeong, J. (2004) EEG Dynamics in Patients with Alzheimer’s Disease. Clinical Neurophysiology, 115, 1490-1505.

[14]   Shaw, R. (1981) Strange Attractors, Chaotic Behavior, and Information Flow. Zeitschrift für Naturforschung A, 36, 80-112.

[15]   Li, X.L., Ouyang, G.X. and Richards, D.A. (2007) Predictability Analysis of Absence Seizures with Permutation Entropy. Epilepsy Research, 77, 70-74.

[16]   Pravin Kumar, S., Sriraam, N. and Benakop, P.G. (2008) Automated Detection of Epileptic Seizures Using Wavelet Entropy Feature with Recurrent Neural Network Classifier. Proceedings of the 2008 IEEE Region 10 Conference of TeNCON, Hyderabad, 19-21 November 2008, 1-5.

[17]   Ocak, H. (2009) Automatic Detection of Epileptic Seizures in EEG Using Discrete Wavelet Transform and Approximate Entropy. Expert Systems with Applications, 36, 2027-2036.

[18]   Ghosh-Dastidar, S., Adeli, H. and Dadmehr, N. (2007) Mixed-Band Wavelet-Chaos-Neural Network Methodology for Epilepsy and Epileptic Seizure Detection. IEEE Transactions on Biomedical Engineering, 54, 1545-1551.

[19]   Alam, S.M.S., Bhuiyan, M.I.H., Aurangozeb and Shahriar, S.T. (2012) EEG Signal Discrimination Using Non-Linear Dynamics in the EMD Domain. International Journal of Computer and Electrical Engineering, 4, 326-330.

[20]   Radhakrishnan, N. and Gangadhar, B.N. (1998) Estimating Regularity in Epileptic Seizure Time Series Data—A Complexity Measure Approach. IEEE Engineering in Medicine and Biology Magazine, 17, 89-94.

[21]   Hu, J., Gao, J. and Principe, J. (2006) Analysis of Biomedical Signals by the Lempel-Ziv Complexity: The Effect of Finite Data Size. IEEE Transactions on Biomedical Engineering, 53, 2606-2609.

[22]   Gao, J., Hu, J. and Tung, W. (2011) Complexity Measures of Brain Wave Dynamics. Cognitive Neurodynamics, 5, 171-182.

[23]   Doyle, T.L.A., Dugan, E.L., Brendan Humphries, B. and Newton, R.U. (2004) Discriminating between Elderly and Young Using a Fractal Dimension Analysis of Centre of Pressure. International Journal of Medical Sciences, 1, 11-20.

[24]   Eckmann, J.P. and Ruelle, D. (1992) Fundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical Systems. Physica D, 56, 185-187.

[25]   Klonowski, W., Stepien, R., Olejarczyk, E., Jernajczyk, W., Niedzielska, K. and Karlinski, A. (1999) Chaotic Quan tifiers of EEG-Signal for Assessing Photo and Chemo-Therapy. Medical & Biological Engineering & Computing, 37, 436-437.

[26]   Andrzejak, R.G., Lehnertz, K., Rieke, C., Mormann, F., David, P. and Elger, C.E. (2001) Indications of Nonlinear Deterministic and Finite Dimensional Structures in Time Series of Brain Electrical Activity: Dependence on Recording Region and Brain State. Physical Review E, 64, Article ID: 061907.

[27]   CHB-MIT Scalp EEG Database [Online].

[28]   Le Van Quyen, M., Foucher, J., Lachaux, J., Rodriguez, E., Lutz, A., Martinerie, J. and Varela, F. (2001) Comparison of Hilbert Transform and Wavelet Methods for the Analysis of Neuronal Synchrony. Journal of Neuroscience Methods, 111, 83-98.

[29]   Quiroga, R.Q., Kraskov, A., Kreuz, T. and Grassberger, P. (2002) Performance of Different Synchronization Measures in Real Data: A Case Study on Electroencephalographic Signals. Physical Review E, 65, 1-15.

[30]   Kamen, P.W. and Tonkin, A.M. (1995) Application of the Poincaré Plot to Heart-Rate-Variability—A New Measure of Functional Status in Heart Failure. Australian and New Zealand Journal of Medicine, 25, 18-26.

[31]   Cohen, M.E., Hudson, D.L. and Deedwania, P.C. (1996) Applying Continuous Chaotic Modeling to Cardiac Signal Analysis. IEEE Engineering in Medicine and Biology Magazine, 15, 97-102.

[32]   Hornero, R., Abásolo, D., Jimeno, N., Sánchez, C.I., Poza, J. and Aboy, M. (2006) Variability, Regularity, and Complexity of Time Series Generated by Schizophrenic Patients and Control Subjects. IEEE Transactions on Biomedical Engineering, 53, 210-218.

[33]   Cohen, M.E. and Hudson, D.L. (2001) Inclusion of ECG and EEG Analysis in Neural Network Models. Proceedings of the 23rd International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2, 1621-1624.

[34]   Thuraisingham, R.A., Tran, Y., Boord, P. and Craig, A. (2007) Analysis of Eyes Open, Eye Closed EEG Signals Using Second-Order Difference Plot. Medical & Biological Engineering & Computing, 45, 1243-1249.

[35]   Zweig, M.H. and Campbell, G. (1993) Receiver-Operating Characteristic (ROC) Plots: A Fundamental Evaluation Tool in Clinical Medicine. Clinical Chemistry, 39, 561-577.

[36]   Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J.D. (1992) Testing for Nonlinearity in Time Series: The Method of Surrogate Data. Physica D, 58, 77-94.

[37]   Rapp, P.E., Cellucci, C.J., Watanabe, T.A.A., Albano, A.M. and Schmah, T.I. (2001) Surrogate Data Pathologies and the False-Positive Rejection of the Null Hypothesis. International Journal of Bifurcation and Chaos, 11, 983-997.

[38]   Stacey, W.C. and Litt, B. (2008) Technology Insight: Neuroengineering and Epilepsy-Designing Devices for Seizure Control. Nature Clinical Practice Neurology, 4, 190-201.

[39]   Richmann, J.S. and Moorman, J.R. (2000) Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy. American Journal of Physiology. Heart and Circulatory Physiology, 278, H2039-H2049.

[40]   Lake, D.E., Richman, J.S., Griffin, M.P. and Moorman, J.R. (2002) Sample Entropy Analysis of Neonatal Heart Rate Variability. American Journal of Physiology. Regulatory, Integrative and Comparative Physiology, 283, R789-R797.

[41]   Ramdani, S., Seigle, B., Lagarde, J., Bouchara, F. and Bernard, P.L. (2009) On the Use of Sample Entropy to Analyze Human Postural Sway Data. Medical Engineering & Physics, 31, 1023-1031.

[42]   Song, Y. and Liò, P. (2010) A New Approach for Epileptic Seizure Detection: Sample Entropy Based Feature Extraction and Extreme Learning Machine. Journal of Biomedical Science and Engineering, 3, 556-567.

[43]   Liang, S., Wang, H. and Chang, W. (2010) Combination of EEG Complexity and Spectral Analysis for Epilepsy Diagnosis and Seizure Detection. EURASIP Journal on Advances in Signal Processing, 2010, 1-15.