Document Type : Full Research Paper


1 Ph.D Student, Bioelectric Department, Biomedical EngineeringFaculty, Islamic Azad University, Science and Research Branch, Tehran, Iran

2 Associate Professor, Biomedical Engineering Department, Engineering Faculty, Islamic Azad University, mashhad Branch, Mashhad, Iran

3 Professor, Bioelectric Department, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran



Using methods based on nonlinear dynamics such as Poincare Section, can be useful in detecting dynamic biological systems. Selecting a suitable Poincare surface is a critical step in data analysis. Often finding an appropriate position for Poincare section needs to set different parameters. When the geometry of Poincare surface picks the information related to the stretching and folding, a better discrimination can be performed for the system states. The objective of this paper is to study the effect of position and degree of Poincare surface in Epileptic Seizure Detection. The Poincare surface resulting in the best classification is selected as the optimal section. Accordingly, the phase space of the EEG Segments Reconstructed in three dimension, firstly. Then, a set of Poincare surfaces with 400 different conditions of degree selected to cut the trajectory and Geometric Features Extracted from the points of intersection on each surface. Afterward, extracted features from the Poincare section are applied to SVM classifier. Pearson correlation analysis was performed to analyze the relationship between the classification performance and degree of Poincare section. Certain behavior can be observed by increasing the Surface degree in output classifier. In this way, the increasing and then decreasing pattern were observed by increasing the Surface degree in two Directions of Surface. The results showed that the equation of optimal Poincare Section for m=12 and n=6 gives the accuracy of 96.6%.


Main Subjects

[1]           ص. لشکری، م.ع. خلیل‌زاده، "مقایسه نتایج حاصل از قطع پوانکاره در فضای فاز دو و سه بعد در تشخیص حملات صرعی "، بیست و یکمین کنفرانس مهندسی برق ایران، دانشگاه فردوسی مشهد، 24-26 اردیبهشت 1392.
[2]           ف. ممشلی، م.ر. هاشمی گلپایگانی، "پردازش غیرخطی سیگنال EEG در حالت توجه به‌منظورپیدا کردن شاخص مناسب برای بیوفیدبک"، پایان‌نامه کارشناسی ارشد، رشته مهندسی پزشکی، گرایش بیوالکتریک، دانشگاه صنعتی امیرکبیر، 1388.
[3]           S. Yang, I. F. Shen, (2007). Manifold analysis in reconstructed state space for nonlinear signal classification. In Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues (pp. 930-937). Springer Berlin Heidelberg.
[4]           J. Jeong, D. J. Kim, J. H. Chae, S. Y. Kim, H. J. Ko, I. H. Paik, (1998). Nonlinear analysis of the EEG of schizophrenics with optimal embedding dimension. Medical engineering & physics, 20(9), 669-676.
[5]           C. J. Stam, (2005). Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clinical Neurophysiology, 116(10), 2266-2301.
[6]           G. Huang, D. Zhang, J. Meng, X. Zhu, (2011). Interactions between two neural populations: A mechanism of chaos and oscillation in neural mass model. Neurocomputing, 74(6), 1026-1034.
[7]           N. V. Thakor, S. Tong, (2004). Advances in quantitative electroencephalogram analysis methods. Annu. Rev. Biomed. Eng., 6, 453-495.
[8]           S. Raiesdana, S. M. R. Hashemi Golpayegani, S. M. P.Firoozabadi, J. Mehvari Habibabadi, (2009). On the discrimination of patho-physiological states in epilepsy by means of dynamical measures. Computers in biology and medicine, 39(12), 1073-1082.
[9]           K. Lehnertz, (2008). Epilepsy and nonlinear dynamics. Journal of biological physics, 34(3-4), 253-266.
[10]         P. A. Coble, D. J. Kupfer, D. G.  Spiker, J. F. Neil, R. J. McPartland, (1979). EEG sleep in primary depression: a longitudinal placebo study. Journal of affective disorders, 1(2), 131-138.
[11]         C. Besthorn, H. Sattel, C. Geiger-Kabisch, R. Zerfass, H. Förstl, (1995). Parameters of EEG dimensional complexity in Alzheimer's disease. Electroencephalography and clinical neurophysiology, 95(2), 84-89.
 [12]        B. Jelles, J. H. Van Birgelen, J. P. J. Slaets, R. E. M. Hekster, E. J. Jonkman, C. J. Stam, (1999). Decrease of non-linear structure in the EEG of Alzheimer patients compared to healthy controls. Clinical Neurophysiology, 110(7), 1159-1167.
[13]         B. Jelles, P. Scheltens, W. M. Van der Flier, E. J. Jonkman, F. H. da Silva, C. J. Stam, (2008). Global dynamical analysis of the EEG in Alzheimer’s disease: frequency-specific changes of functional interactions. Clinical Neurophysiology, 119(4), 837-841.
[14]         G. Hori, K. Aihara, Y. Mizuno, Y. Okuma, (2001). Blind source separation and chaotic analysis of EEG for judgment of brain death. Artificial Life and Robotics, 5(1), 10-14.
[15]         C. C. Liu, P. M. Pardalos, W. A. Chaovalitwongse, D. S. Shiau, G. Ghacibeh, W. Suharitdamrong, J. C. Sackellares, (2008). Quantitative complexity analysis in multi-channel intracranial EEG recordings form epilepsy brains. Journal of combinatorial optimization, 15(3), 276-286.
[16]         A. Casaleggio, S. Braiotta, A. Corana, (1995, September). Study of the Lyapunov exponents of ECG signals from MIT-BIH database. In Computers in Cardiology 1995 (pp. 697-700). IEEE.
[17]         E. D. Ubeyli, (2009). Modified mixture of experts employing eigenvector methods and Lyapunov exponents for analysis of electroencephalogram signals. Expert Systems, 26(4), 339-354.
[18]         N. Kannathal, U. R. Acharya, C. M. Lim, P. K. Sadasivan, (2005). Characterization of EEG—a comparative study. Computer methods and Programs in Biomedicine, 80(1), 17-23.
[19]         D. P. Subha, P. K. Joseph, R. Acharya, C. M. Lim, (2010). EEG signal analysis: A survey. Journal of medical systems, 34(2), 195-212.
[20]         R. Cerf, M. El Amri, E. H. El Ouasdad, E. Hirsch, (1999). Non-linear analysis of epileptic seizures I. Correlation-dimension measurements for absence epilepsy and near-periodic signals. Biological cybernetics, 80(4), 247-258.
[21]         G. E. Polychronaki, P. Y. Ktonas, S. Gatzonis, A. Siatouni, P. A. Asvestas, H. Tsekou, K. S. Nikita, (2010). Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection. Journal of neural engineering, 7(4), 046007.
[22]         D. Easwaramoorthy, R. Uthayakumar, (2011). Improved generalized fractal dimensions in the discrimination between healthy and epileptic EEG signals. Journal of Computational Science, 2(1), 31-38.
[23]         P. Paramanathan, R. Uthayakumar, (2008). Application of fractal theory in analysis of human electroencephalographic signals. Computers in Biology and medicine, 38(3), 372-378.
[24]         R. Hilborn, (2000). Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford university press.
[25]         G. Kubin, (1997, September). Poincaré section techniques for speech. InSpeech Coding for Telecommunications Proceeding, 1997, 1997 IEEE Workshop on (pp. 7-8). IEEE.
[26]         I. Mann, S. McLaughlin, (1997, December). Poincare maps and pitch detection in speech. In Signals Systems and Chaos (Ref. No. 1997/393), IEE Colloquium on (pp. 5-1). IET.
[27]         S. Yang, (2004). Nonlinear signal classification using geometric statistical features in state space. Electronics Letters, 40(12), 780-781.
[28]         S. Yang, (2005). Nonlinear signal classification in the framework of high-dimensional shape analysis in reconstructed state space. Circuits and Systems II: Express Briefs, IEEE Transactions on, 52(8), 512-516.
[29]         A. Goshvarpour, A. Goshvarpour, S. Rahati, (2011). Analysis of lagged Poincare plots in heart rate signals during meditation. Digital Signal Processing, 21(2), 208-214.
[30]         T. A. Denton, G. A. Diamond, R. H. Helfant, S. Khan,  H. Karagueuzian, (1990). Fascinating rhythm: a primer on chaos theory and its application to cardiology. American heart journal, 120(6), 1419-1440.
[31]         S. Parvaneh, M. R. Hashemi Golpayegani, M. Firoozabadi, M. Haghjoo, (2012). Predicting the spontaneous termination of atrial fibrillation based on Poincare section in the electrocardiogram phase space. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 226(1), 3-20.
[32]         H. Kantz, T. Schreiber, (2004). Nonlinear time series analysis (Vol. 7). Cambridge university press.
[33]         A. Brignol, A. Tarik, "Phase space and power spectral approaches for EEG-based automatic sleep–wake classification in humans: A comparative study using short and standard epoch lengths." computer methods and programs in biomedicine (2013).
 [34]        R. G. Andrzejak, K. Lehnertz, F. Mormann, C. Rieke, P. David, C. E. Elger, (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(6), 061907.
[35]         A. Paraschiv-Ionescu, K. Aminian, (2009). Nonlinear analysis of physiological time series. In Advanced biosignal processing (pp. 307-333). Springer Berlin Heidelberg.
[36]         M. Akay, (2001). Nonlinear Biomedical Signal Processing, Vol 2: Dynamic Analysis and Modeling. IEEE press.
[37]         A. M. Fraser, H. L. Swinney, (1986). Independent coordinates for strange attractors from mutual information. Physical review A, 33(2), 1134.
[38]         R. Hegger, H. Kantz, T. Schreiber, (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos: An Interdisciplinary Journal of Nonlinear Science, 9(2), 413-435.
[39]         A. M. Climent, M. S. Guillem, D. Husser, F. J. Castells, J. Millet, A. Bollmann, (2007, September). Poincaré surface profile. Novel non-invasive method to detect preferential ventricular response during atrial fibrillation. InComputers in Cardiology, 2007 (pp. 585-588). IEEE.
[40]         S. C. Fang, H. L. Chan, (2009). Human identification by quantifying similarity and dissimilarity in electrocardiogram phase space. Pattern Recognition, 42(9), 1824-1831.
[41]         W. P. Garnett, (1997). Chaos theory tamed. Chaos theory tamed.
[42]         C. J. Burges, (1998). A tutorial on support vector machines for pattern recognition. Data mining and knowledge discovery, 2(2), 121-167.
[43]         R. R. Sun, Y. Y. Wang (2009). Predicting spontaneous termination of atrial fibrillation based on the RR interval. Proc Inst Mech Eng H 223 (6): 713-26.
[44]         S. Jafari, S. M. R. Hashemi Golpayegani, and A. H. Jafari. (2012)"A novel noise reduction method based on geometrical properties of continuous chaotic signals." Scientia Iranica.