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EEG Signal Processing and Feature Extraction pp 215–240Cite as

Nonlinear Neural Dynamics

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Abstract

Brain activities measured by EEG exhibit complex behavior with nonlinear dynamic properties. Therefore, methods derived from nonlinear theory could contribute to the understanding of the EEG dynamics and the underlying brain processes. Until now, a number of nonlinear dynamic methods have been proposed. These methods reveal various nonlinear properties of the EEG signals. Among them, “complexity” and “entropy” are the widely used concept in the EEG analysis. Moreover, entropy-based measures have been applied into clinical practice of monitoring depth of anesthesia. This study selects three classical types of nonlinear dynamic measures (total 12), introducing their basic theory and giving examples of applying them in real EEG analysis. All the MATLAB codes can be downloaded from https://pan.baidu.com/s/1ro2VEJWdsb5X6dCtueGUOA with password: hf4x. Although previous studies compared the performance of various nonlinear dynamic measures at different situations, it is still improper to determine which measure is the best one. The measure selection in your study should take a number of factors into account, such as the parameter selection, robust to artifacts, compute consumption, the correlation of the nonlinear characteristics with the underlying neural process, and so on.

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References

  • Abasolo D, Hornero R, Gomez C, Garcia M, Lopez M. Analysis of EEG background activity in Alzheimer’s disease patients with Lempel-Ziv complexity and central tendency measure. Med Eng Phys. 2006;28(4):315–22. https://doi.org/10.1016/j.medengphy.2005.07.004.

    Article  PubMed  Google Scholar 

  • Aboy M, Hornero R, Abasolo D, Alvarez D. Interpretation of the Lempel-Ziv complexity measure in the context of biomedical signal analysis. IEEE Trans Biomed Eng. 2006;53(11):2282–8. https://doi.org/10.1109/TBME.2006.883696.

    Article  PubMed  Google Scholar 

  • Anier A, Lipping T, Jantti V, Puumala P, Huotari A Entropy of the EEG in transition to burst suppression in deep anesthesia: surrogate analysis. In: Engineering in medicine and biology society (EMBC), 2010 annual international conference of the IEEE, 2010. IEEE, pp. 2790–3.

    Google Scholar 

  • Bai Y, Liang Z, Li X. A permutation Lempel-Ziv complexity measure for EEG analysis. Biomed Signal Process Control. 2015;19:102–14.

    Article  Google Scholar 

  • Bandt C. Ordinal time series analysis. Ecol Model. 2005;182(3):229–38.

    Article  Google Scholar 

  • Bandt C, Pompe B. Permutation entropy: a natural complexity measure for time series. Phys Rev Lett. 2002a;88(17):174102.

    Article  PubMed  Google Scholar 

  • Bandt C, Pompe B. Permutation entropy: a natural complexity measure for time series. Phys Rev Lett. 2002b;88(17):174102.

    Article  PubMed  Google Scholar 

  • Bein B. Entropy. Best Pract Res Clin Anaesthesiol. 2006;20(1):101–9.

    Article  CAS  PubMed  Google Scholar 

  • Bruhn J, Lehmann LE, Röpcke H, Bouillon TW, Hoeft A. Shannon entropy applied to the measurement of the electroencephalographic effects of desflurane. Anesthesiology. 2001;95(1):30–5.

    Article  CAS  PubMed  Google Scholar 

  • Bruhn J, Röpcke H, Hoeft A. Approximate entropy as an electroencephalographic measure of anesthetic drug effect during desflurane anesthesia. Anesthesiology. 2000;92(3):715–26.

    Article  CAS  PubMed  Google Scholar 

  • Bruzzo AA, Gesierich B, Santi M, Tassinari CA, Birbaumer N, Rubboli G. Permutation entropy to detect vigilance changes and preictal states from scalp EEG in epileptic patients. A preliminary study. Neurol Sci. 2008;29(1):3–9. https://doi.org/10.1007/s10072-008-0851-3.

    Article  PubMed  Google Scholar 

  • Cao Y, Tung W, Gao J, Protopopescu V, Hively L. Detecting dynamical changes in time series using the permutation entropy. Phys Rev E. 2004a;70(4; Part 2):46217.

    Article  Google Scholar 

  • Cao Y, Tung WW, Gao JB, Protopopescu VA, Hively LM. Detecting dynamical changes in time series using the permutation entropy. Phys Rev E Stat Nonlinear Soft Matter Phys. 2004b;70(4. Pt 2):046217.

    Article  Google Scholar 

  • Chen CC, Hsu YT, Chan HL, Chiou SM, Tu PH, Lee ST, Tsai CH, Lu CS, Brown P. Complexity of subthalamic 13-35 Hz oscillatory activity directly correlates with clinical impairment in patients with Parkinson’s disease. Exp Neurol. 2010;224(1):234–40. https://doi.org/10.1016/j.expneurol.2010.03.015.

    Article  PubMed  Google Scholar 

  • Chen W, Zhuang J, Yu W, Wang Z. Measuring complexity using FuzzyEn, ApEn, and SampEn. Med Eng Phys. 2009;31(1):61–8.

    Article  PubMed  Google Scholar 

  • Dauwels J, Srinivasan K, Ramasubba Reddy M, Musha T, Vialatte FB, Latchoumane C, Jeong J, Cichocki A. Slowing and loss of complexity in Alzheimer’s EEG: two sides of the same coin? Int J Alzheimers Dis. 2011;2011:539621. https://doi.org/10.4061/2011/539621.

    Article  PubMed  PubMed Central  Google Scholar 

  • Eckmann JP, Kamphorst SO, Ruelle D. Recurrence plots of dynamical systems. EPL (Europhys Lett). 1987;4:973.

    Article  Google Scholar 

  • Facchini A, Mocenni C, Marwan N, Vicino A, Tiezzi E. Nonlinear time series analysis of dissolved oxygen in the Orbetello lagoon (Italy). Ecol Model. 2007;203(3–4):339–48.

    Article  Google Scholar 

  • Hu J, Gao J, Príncipe JC. Analysis of biomedical signals by the Lempel-Ziv complexity: the effect of finite data size. IEEE Trans Biomed Eng. 2006;53(12):2606–9.

    Article  PubMed  Google Scholar 

  • Huang L, Yu P, Ju F, Cheng J. Prediction of response to incision using the mutual information of electroencephalograms during anaesthesia. Med Eng Phys. 2003;25(4):321–7.

    Article  CAS  PubMed  Google Scholar 

  • Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc Roy Soc Lond A. 1998;454(1971):903–95.

    Article  Google Scholar 

  • Inouye T, Shinosaki K, Sakamoto H, Toi S, Ukai S, Iyama A, Katsuda Y, Hirano M. Quantification of EEG irregularity by use of the entropy of the power spectrum. Electroencephalogr Clin Neurophysiol. 1991;79(3):204–10.

    Article  CAS  PubMed  Google Scholar 

  • Jouny CC, Bergey GK. Characterization of early partial seizure onset: frequency, complexity and entropy. Clin Neurophysiol. 2012;123(4):658–69. https://doi.org/10.1016/j.clinph.2011.08.003.

    Article  PubMed  Google Scholar 

  • Klaus B, Gerhard S, Matthias E, Andreas R, Kochs EF, Walter Z, Hans-Ulrich D. Anaesthesia monitoring by recurrence quantification analysis of EEG data. PLoS One. 2010;5(1):e8876.

    Article  Google Scholar 

  • Klockars JG, Hiller A, Munte S, van Gils MJ, Taivainen T. Spectral entropy as a measure of hypnosis and hypnotic drug effect of total intravenous anesthesia in children during slow induction and maintenance. Anesthesiology. 2012;116(2):340–51. https://doi.org/10.1097/ALN.0b013e3182410b5e.

    Article  CAS  PubMed  Google Scholar 

  • Lempel A, Ziv J. On the complexity of finite sequences. IEEE Trans Inf Theory. 1976;22(1):75–81.

    Article  Google Scholar 

  • Li D, Li X, Liang Z, Voss LJ, Sleigh JW. Multiscale permutation entropy analysis of EEG recordings during sevoflurane anesthesia. J Neural Eng. 2010;7(4):046010.

    Article  PubMed  Google Scholar 

  • Li X. Temporal structure of neuronal population oscillations with empirical model decomposition. Phys Lett A. 2006;356(3):237–41.

    Article  CAS  Google Scholar 

  • Li X, Cui S, Voss LJ. Using permutation entropy to measure the electroencephalographic effects of sevoflurane. Anesthesiology. 2008a;109(3):448.

    Article  CAS  PubMed  Google Scholar 

  • Li X, Li D, Liang Z, Voss LJ, Sleigh JW. Analysis of depth of anesthesia with Hilbert–Huang spectral entropy. Clin Neurophysiol. 2008b;119(11):2465–75. https://doi.org/10.1016/j.clinph.2008.08.006.

    Article  PubMed  Google Scholar 

  • Li X, Ouyang G, Richards DA. Predictability analysis of absence seizures with permutation entropy. Epilepsy Res. 2007;77(1):70.

    Article  PubMed  Google Scholar 

  • Li X, Ouyang G, Yao X, Guan X. Dynamical characteristics of pre-epileptic seizures in rats with recurrence quantification analysis. Phys Lett A. 2004;333(1–2):164–71.

    Article  CAS  Google Scholar 

  • Li XL, Cui SY, Voss LJ. Using permutation entropy to measure the electroencephalographic effects of sevoflurane. Anesthesiology. 2008c;109(3):448–56. https://doi.org/10.1097/Aln.0b013e318182a91b.

    Article  CAS  PubMed  Google Scholar 

  • Li XL, Ouyang GX. Estimating coupling direction between neuronal populations with permutation conditional mutual information. NeuroImage. 2010;52(2):497–507. https://doi.org/10.1016/j.neuroimage.2010.05.003.

    Article  PubMed  Google Scholar 

  • 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. Clin Neurophysiol. 2008d;119(6):1232–41. https://doi.org/10.1016/j.clinph.2008.01.104.

    Article  PubMed  Google Scholar 

  • Li Z, Li X. Estimating temporal causal interaction between spike trains with permutation and transfer entropy. PLoS One. 2013;8(8):e70894.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Liang H, Lin Z, McCallum R. Artifact reduction in electrogastrogram based on empirical mode decomposition method. Med Biol Eng Comput. 2000;38(1):35–41.

    Article  CAS  PubMed  Google Scholar 

  • Liang Z, Li D, Ouyang G, Wang Y, Voss LJ, Sleigh JW, Li X. Multiscale rescaled range analysis of EEG recordings in sevoflurane anesthesia. Clin Neurophysiol. 2012;123(4):681–8.

    Article  PubMed  Google Scholar 

  • Liang Z, Wang Y, Sun X, Li D, Voss LJ, Sleigh JW, Hagihira S, Li X. EEG entropy measures in anesthesia. Front Comput Neurosci. 2015;9:16.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Linde Y, Buzo A, Gray RM. Algorithm for vector Quantizer design. Ieee T Commun. 1980;28(1):84–95. https://doi.org/10.1109/Tcom.1980.1094577.

    Article  Google Scholar 

  • Marwan N. Encounters with neighbours: current developments of concepts based on recurrence plots and their applications. Norbert Marwan; 2003.

    Google Scholar 

  • Marwan N, Romano MC, Thiel M, Kurths J. Recurrence plots for the analysis of complex systems. Phys Rep. 2007;438(5):237–329.

    Article  Google Scholar 

  • Matic V, Cherian PJ, Koolen N, Ansari AH, Naulaers G, Govaert P, Huffel SV, Vos MD, Vanhatalo S (2015) Objective differentiation of neonatal EEG background grades using detrended fluctuation analysis. Front Hum Neurosci 9:189.

    Google Scholar 

  • Mocenni C, Stanley HE. Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties. Proc Natl Acad Sci U S A. 2010;107(18):8097–102.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Olofsen E, Sleigh JW, Dahan A. Permutation entropy of the electroencephalogram: a measure of anaesthetic drug effect. Br J Anaesth. 2008;101(6):810–21. https://doi.org/10.1093/bja/aen290.

    Article  CAS  PubMed  Google Scholar 

  • Ouyang G, Li X, Dang C, Richards DA. Using recurrence plot for determinism analysis of EEG recordings in genetic absence epilepsy rats. Clin Neurophysiol. 2008;119(8):1747–55.

    Article  PubMed  Google Scholar 

  • Pincus SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci. 1991;88(6):2297–301.

    Article  CAS  PubMed  Google Scholar 

  • Röschke J, Fell J, Beckmann P. Nonlinear analysis of sleep eeg in depression: calculation of the largest lyapunov exponent. Eur Arch Psychiatry Clin Neurosci. 1995;245(1):27–35.

    Article  PubMed  Google Scholar 

  • Rajendra AU, Faust O, Kannathal N, Chua TL, Laxminarayan S. Non-linear analysis of EEG signals at various sleep stages. Comput Methods Programs Biomed. 2005;80(1):37–45.

    Article  Google Scholar 

  • Richman JS, Moorman JR. Physiological time-series analysis using approximate entropy and sample entropy. Am J Phys Heart Circ Phys. 2000;278(6):H2039–49.

    CAS  Google Scholar 

  • Rilling G, Flandrin P, Gonçalvés P. On empirical mode decomposition and its algorithms. In: IEEE-EURASIP workshop on nonlinear signal and image processing, NSIP-03, Grado (I), 2003.

    Google Scholar 

  • Rosso OA, Blanco S, Yordanova J, Kolev V, Figliola A, Schurmann M, Basar E. Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J Neurosci Methods. 2001;105(1):65–76.

    Article  CAS  PubMed  Google Scholar 

  • Särkelä MOK, Ermes MJ, van Gils MJ, Yli-Hankala AM, Jäntti VH, Vakkuri AP. Quantification of epileptiform electroencephalographic activity during sevoflurane mask induction. Anesthesiology. 2007;107(6):928–38.

    Article  PubMed  Google Scholar 

  • Sabeti M, Katebi S, Boostani R. Entropy and complexity measures for EEG signal classification of schizophrenic and control participants. Artif Intell Med. 2009;47(3):263–74.

    Article  PubMed  Google Scholar 

  • Schinkel S, Marwan N, Kurths J. Brain signal analysis based on recurrences. J Physiol Paris. 2009;103(6):315–23.

    Article  PubMed  Google Scholar 

  • Schultz A, Siedenberg M, Grouven U, Kneif T, Schultz B. Comparison of Narcotrend index, Bispectral index, spectral and entropy parameters during induction of propofol-remifentanil anaesthesia. J Clin Monit Comput. 2008;22(2):103–11. https://doi.org/10.1007/s10877-008-9111-6.

    Article  PubMed  Google Scholar 

  • Shalbaf R, Behnam H, Sleigh JW, Voss LJ. Using the Hilbert–Huang transform to measure the electroencephalographic effect of propofol. Physiol Meas. 2012;33(2):271–85. https://doi.org/10.1088/0967-3334/33/2/271.

    Article  CAS  PubMed  Google Scholar 

  • Shannon CE. A mathematical theory of communication, Bell System. New York: American Telephone and Telegraph Co.; 1922.

    Google Scholar 

  • Shannon CE, Weaver W. The mathematical theory of communication. Urbana: University of Illinois Press; 1949.

    Google Scholar 

  • Shayegh F, Sadri S, Amirfattahi R, Ansari-Asl K. A model-based method for computation of correlation dimension, Lyapunov exponents and synchronization from depth-EEG signals. Comput Methods Programs Biomed. 2014;113(1):323–37.

    Article  CAS  PubMed  Google Scholar 

  • Sleigh J, Voss L, Barnard J. What are electroencephalogram entropies really measuring? Int Congr Ser. 2005;1283:231–4. https://doi.org/10.1016/j.ics.2005.06.048.

    Article  CAS  Google Scholar 

  • Sleigh JW, Olofsen E, Dahan A, De Goede J, Steyn-Ross DA (2001) Entropies of the EEG: the effects of general anaesthesia.

    Google Scholar 

  • Song IH, Lee DS, Kim SI. Recurrence quantification analysis of sleep electoencephalogram in sleep apnea syndrome in humans. Neurosci Lett. 2004;366(2):148–53.

    Article  CAS  PubMed  Google Scholar 

  • Takens F. Dynamical systems and turbulence. Lecture Notes in Mathematics. 1981;898(9):366.

    Article  Google Scholar 

  • Viertiö-Oja H, Maja V, Särkelä M, Talja P, Tenkanen N, Tolvanen-Laakso H, Paloheimo M, Vakkuri A, Yli-Hankala A, Meriläinen P. Description of the Entropy™ algorithm as applied in the Datex-Ohmeda S/5™ Entropy Module. Acta Anaesthesiol Scand. 2004;48(2):154–61.

    Article  PubMed  Google Scholar 

  • Webber JC, Zbilut JP. Dynamical assessment of physiological systems and states using recurrence plot strategies. J Appl Physiol. 1994;76(2):965.

    Article  PubMed  Google Scholar 

  • Worrell GA, Cranstoun SD, Echauz J, Litt B. Evidence for self-organized criticality in human epileptic hippocampus. Neuroreport. 2002;13(16):2017.

    Article  PubMed  Google Scholar 

  • Yan J, Wang Y, Ouyang G, Yu T, Li Y, Sik A, Li X. Analysis of electrocorticogram in epilepsy patients in terms of criticality. Nonlinear Dyn. 2016;83(4):1909–17.

    Article  Google Scholar 

  • Yoon YG, Kim TH, Jeong DW, Park SH. Monitoring the depth of anesthesia from rat EEG using modified Shannon entropy analysis. Conf Proc IEEE Eng Med Biol Soc. 2011;2011:4386–9. https://doi.org/10.1109/IEMBS.2011.6091088.

    Article  PubMed  Google Scholar 

  • Zhang HX, Zhu YS, Wang ZM. Complexity measure and complexity rate information based detection of ventricular tachycardia and fibrillation. Med Biol Eng Comput. 2000;38(5):553–7.

    Article  CAS  PubMed  Google Scholar 

  • Zhang X-S, Roy RJ, Jensen EW. EEG complexity as a measure of depth of anesthesia for patients. IEEE Trans Biomed Eng. 2001;48(12):1424–33.

    Article  CAS  PubMed  Google Scholar 

  • Zhang XS, Roy RJ. Derived fuzzy knowledge model for estimating the depth of anesthesia. IEEE Trans Biomed Eng. 2001;48(3):312–23. https://doi.org/10.1109/10.914794.

    Article  CAS  PubMed  Google Scholar 

  • Zhou S, Zhang Z, Gu J Interpretation of coarse-graining of Lempel-Ziv complexity measure in ECG signal analysis. Conference proceedings: annual international conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society conference 2011: pp. 2716–2719; 2011. https://doi.org/10.1109/IEMBS.2011.6090745.

  • Zoughi T, Boostani R, Deypir M. A wavelet-based estimating depth of anesthesia. Eng Appl Artif Intell. 2012;25(8):1710–22. https://doi.org/10.1016/j.engappai.2011.10.006.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Basic Medical Science, School of Medicine, Hangzhou Normal University, Hangzhou, Zhejiang, China

    Yang Bai

  2. State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China

    Xiaoli Li

  3. Institute of Electric Engineering, Yanshan University, Qinhuangdao, Hebei, China

    Zhenhu Liang

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  1. Yang Bai
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  2. Xiaoli Li
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  3. Zhenhu Liang
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Correspondence to Yang Bai .

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Editors and Affiliations

  1. CAS Key Laboratory of Mental Health, Institute of Psychology, Chinese Academy of Sciences, Beijing, China

    Li Hu

  2. School of Biomedical Engineering, Health Science Center, Shenzhen University, Shenzhen, Guangdong, China

    Zhiguo Zhang

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Bai, Y., Li, X., Liang, Z. (2019). Nonlinear Neural Dynamics. In: Hu, L., Zhang, Z. (eds) EEG Signal Processing and Feature Extraction. Springer, Singapore. https://doi.org/10.1007/978-981-13-9113-2_11

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