Identification of focal epileptic regions from electroencephalographic data: Feigenbaum graphs

G. Guarneros, C. Pérez, A. Montiel, J. F. Rojas

Abstract


In the study of problems related to epilepsy analyzing electroencephalograms data is of much importance to help, one hand, to its diagnosis, and, another hand in the possibility of diminishing errors in surgery. We do this analysis making the Feigenbaum graphs for real electroencephalographic signals data sets and calculating characteristic networks (graph) quantities, such as average clustering, degree distribution, and average shortest path length. 
We manage to characterize two different data sets from each other, from data sets corresponding to focal and non-focal neuronal activity both time out of an epileptic seizure. This method enables us to identify sets of data from epileptic focal zones and suggest our approach could be used to aid physicians with diagnosing epilepsy from electroencephalographic data and/or in an exact establishment of the epileptic focal region for surgery.


Keywords


EEG, Epilepsy, Statistical Physics methods, Feigenbaum graphs, visibility graph

Full Text:

PDF

References


Epilepsy Foundation. https://www.epilepsy.com/. Accessed: 2018-08-27.

Deborah Buck, Gus A Baker, Ann Jacoby, David F Smith, and David W Chadwick. Patients’ Experiences of Injury as a Result of Epilepsy. Epilepsia, 38(4):439–444, 1997.

N M G Bodde, J L Brooks, G A Baker, P A J M Boon, J G M Hendriksen, O G Mulder, and A P Aldenkamp. Psychogenic non-epileptic seizures–definition, etiology, treatment and prognostic issues: a critical review. Seizure, 18(8):543–553, October 2009.

M. Bandarabadi, J. Rasekhi, C. A. Teixeira, M. R. Karami, and

A. Dourado. On the proper selection of preictal period for seizure prediction. Epilepsy Behav, 46:158–166, May 2015.

C. Zhou, L. Zemanova, G. Zamora, C. C. Hilgetag, and J. Kurths. Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett., 97(23):238103, Dec 2006.

Leone Ridsdale. Avoiding premature death in epilepsy. BMJ, 350, 2015. Brian Y. Weinshenker, and Jerry S. Wolinsky. Recommended diagnostic criteria for multiple sclerosis: Guidelines from the international panel on the diagnosis of multiple sclerosis. Annals of Neurology, 50(1):121–127.

Srimonti Dutta, Dipak Ghosh, Shukla Samanta, and Santanu Dey. Multifractal parameters as an indication of different physiological and pathological states of the human brain. Physica A: Statistical Mechanics and its Applications, 396:155–163, 2014.

Klaus Lehnertz, Gerrit Ansmann, Stephan Bialonski, Henning Dickten, Christian Geier, and Stephan Porz. Evolving networks in the human epileptic brain. Physica D: Nonlinear Phenomena, 267:7–15, 2014. Evolving Dynamical Networks.

L. Kuhlmann, P. Karoly, D. R. Freestone, B. H. Brinkmann, A. Temko, A. Barachant, F. Li, G. Titericz, B. W. Lang, D. Lavery, K. Roman, D. Broadhead, S. Dobson, G. Jones, Q. Tang, I. Ivanenko, O. Panichev, T. Proix, M. Nahlik, D. B. Grunberg, C. Reuben, G. Worrell, B. Litt, D. T. J. Liley, D. B. Grayden, and M. J. Cook. Epilepsyecosystem.org: crowd-sourcing reproducible seizure prediction with long-term human intracranial EEG. Brain, Aug 2018.

M. R. Nuwer. The development of EEG brain mapping. J Clin Neurophysiol, 7(4):459–471, Oct 1990.

Dipak Ghosh, Srimonti Dutta, and Sayantan Chakraborty. Multifractal detrended cross-correlation analysis for epileptic patient in seizure and seizure free status. Chaos, Solitons & Fractals, 67:1–10, 2014.

Ralph G. Andrzejak, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Peter David, and Christian E. Elger. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Phys. Rev. E, 64:061907, Nov 2001.

Oliver Faust, U. Rajendra Acharya, Hojjat Adeli, and Amir Adeli. Wavelet-based EEG processing for computer-aided seizure detection and epilepsy diagnosis. Seizure, 26:56–64, 2015.

Sheng-Fu Liang, Hsu-Chuan Wang, and Wan-Lin Chang. Combination of EEG Complexity and Spectral Analysis for Epilepsy Diagnosis and 17 Seizure Detection. EURASIP J. Adv. Signal Process, 2010:62:1–62:15, February 2010.

U. Rajendra Acharya, S. Vinitha Sree, G. Swapna, Roshan Joy Martis, and Jasjit S. Suri. Automated EEG analysis of epilepsy: A review. Knowledge-Based Systems, 45:147–165, 2013.

Mehran Ahmadlou, Anahita Adeli, Ricardo Bajo, and Hojjat Adeli. Complexity of functional connectivity networks in mild cognitive impairment subjects during a working memory task. Clinical Neurophysiology, 125(4):694–702, 2014.

U. R. Acharya, V. K. Sudarshan, H. Adeli, J. Santhosh, J. E. Koh, and A. Adeli. Computer-Aided Diagnosis of Depression Using EEG Signals. Eur. Neurol., 73(5-6):329–336, 2015.

R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, New York: John Wiley & Sons, 2001, pp. xx 654, ISBN: 0-471-05669-3. J. Classification, 24(2):305–307, 2007.

P Welch. The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust., 15(2):70–73, June 1967.

A. Scheffler, D. Telesca, Q. Li, C. A. Sugar, C. Distefano, S. Jeste, and D. Senturk. Hybrid principal components analysis for region-referenced longitudinal functional EEG data. Biostatistics, Aug 2018.

H. Adeli, Z. Zhou, and N. Dadmehr. Analysis of EEG records in an epileptic patient using wavelet transform. J. Neurosci. Methods, 123(1):69–87, Feb 2003.

S. Ghosh-Dastidar, H. Adeli, and N. Dadmehr. Mixed-Band WaveletChaos-Neural Network Methodology for Epilepsy and Epileptic Seizure Detection. IEEE Transactions on Biomedical Engineering, 54(9):1545–1551, Sept 2007.

Z. Czechowski, M. Lovallo, and L. Telesca. Multifractal analysis of visibility graph-based Ito-related connectivity time series. Chaos, 26(2):023118, Feb 2016.

U Rajendra Acharya, Hamido Fujita, Vidya K Sudarshan, Shreya Bhat, and Joel En Wei Koh. Application of entropies for automated diagnosis of epilepsy using EEG signals: A review. 88, 08 2015.

G. Ouyang, J. Li, X. Liu, and X. Li. Dynamic characteristics of absence EEG recordings with multiscale permutation entropy analysis. Epilepsy Res., 104(3):246–252, May 2013.

M Vetterli and C Herley. Wavelets and filter banks: theory and design. IEEE Trans. Signal Process., 40(9):2207–2232, 1992.

Juan P. Amezquita-Sanchez and Hojjat Adeli. A New Music-empirical Wavelet Transform Methodology for Time-frequency Analysis of Noisy Nonlinear and Non-stationary Signals. Digit. Signal Process., 45(C):55–68, October 2015.

Zhong-Ke Gao, Qing Cai, Yu-Xuan Yang, Na Dong, and Shan-Shan Zhang. Visibility Graph from Adaptive Optimal Kernel Time-Frequency Representation for Classification of Epileptiform EEG. Int. J. Neural Syst., 27(4):1750005, June 2017.

Guohun Zhu, Yan Li, and Peng Paul Wen. Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal. IEEE J Biomed Health Inform, 18(6):1813–1821, November 2014.

Deng Wang, Duoqian Miao, and Chen Xie. Best basis-based wavelet packet entropy feature extraction and hierarchical EEG classification for epileptic detection. Expert Syst. Appl., 2011.

Ralph G Andrzejak, Kaspar Schindler, and Christian Rummel. Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 86(4 Pt 2):046206, October 2012.

A. L. Barab´asi. Network Science, http://networksciencebook.com/, Common Creative.

Zhong-Ke Gao, Yu-Xuan Yang, Peng-Cheng Fang, Yong Zou, Cheng-Yi Xia, and Meng Du. Multiscale complex network for analyzing experimental multivariate time series. 109, 02 2015.

S. Bhaduri and D. Ghosh. Electroencephalographic Data Analysis With Visibility Graph Technique for Quantitative Assessment of Brain Dysfunction. Clin EEG Neurosci, 46(3):218–223, Jul 2015.

Xiaoke Xu, Jie Zhang, and Michael Small. Superfamily phenomena and motifs of networks induced from time series. Proc. Natl. Acad. Sci. U. S. A., 105(50):19601–19605, December 2008.

Lucas Lacasa and Raul Toral. Description of stochastic and chaotic series using visibility graphs. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 82(3 Pt 2):036120, September 2010.

Bartolo Luque, Lucas Lacasa, Fernando J Ballesteros, and Alberto Robledo. Feigenbaum graphs: a complex network perspective of chaos. PLoS One, 6(9):e22411, September 2011.

Zhong-Ke Gao and Ning-De Jin. A directed weighted complex network for characterizing chaotic dynamics from time series. Nonlinear Analysis: Real World Applications, 13(2):947–952, 2012.

Jari Saram¨aki, Mikko Kivel¨a, Jukka-Pekka Onnela, Kimmo Kaski, and J´anos Kert´esz. Generalizations of the clustering coefficient to weighted complex networks. Phys. Rev. E, 75:027105, Feb 2007.

Marcus Kaiser. Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. New Journal of Physics, 10(8):083042, 2008.

Jukka-Pekka Onnela, Jari Saram¨aki, J´anos Kert´esz, and Kimmo Kaski. Intensity and coherence of motifs in weighted complex networks. Phys. Rev. E, 71:065103, Jun 2005.

Danny Z. Chen. Developing Algorithms and Software for Geometric Path Planning Problems. ACM Comput. Surv., 28(4es), December 1996. https://www.overleaf.com/7311793827cfdkytqdjrjc




DOI: https://doi.org/10.31349/RevMexFis.67.324

Refbacks

  • There are currently no refbacks.


REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

The responsibility of the materials published in Revista Mexicana de Física rests solely with their authors and their content does not necessarily reflect the criteria of the Editorial Committee or the Sociedad Mexicana de Física. The total or partial reproduction of the texts hereby published is authorized as long as the complete source and the electronic address of the publications are cited.

There is no fee for article processing, submission or publication.

Revista Mexicana de Física by Sociedad Mexicana de Física, A. C. is distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License