Entropy Measures in Neural Signals



Entropy measures have been widely used in analyzing neural signals from micro- to macroscales for the normal or abnormal brain assessment. As it is unrealistic to systematic analysis in all the information entropy-based indices in different application areas within limited chapters, we mainly focus on the comparison of the capability of 12 entropy indices derived from electroencephalogram (EEG) for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents.

Twelve indices were included: response entropy (RE) and state entropy (SE); three wavelet entropy (WE) measures (Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)); Hilbert–Huang spectral entropy (HHSE); approximate entropy (ApEn); sample entropy (SampEn); Fuzzy entropy (FuzzyEn); and three permutation entropy (PE) measures (Shannon PE (SPE), Tsallis PE (TPE), and Renyi PE (RPE)). Two EEG data sets recorded from sevoflurane-induced and isoflurane-induced anesthesia, respectively, were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (P k ) analysis were applied.

All the entropy indices could track the changes of anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; while ApEn and SampEn discriminated BSP best.

Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index has a superior performance. Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.


EEG Anesthesia Entropy Pharmacokinetic/Pharmacodynamic modeling Depth of anesthesia 


  1. Abásolo D, et al. Entropy analysis of the EEG background activity in Alzheimer’s disease patients. Physiol Meas. 2006;27(3):241.PubMedCrossRefGoogle Scholar
  2. Ahmed MU, Mandic DP. Multivariate multiscale entropy: a tool for complexity analysis of multichannel data. Phys Rev E. 2011;84(6):061918.CrossRefGoogle Scholar
  3. Arefian NM, et al. Clinical analysis of eeg parameters in prediction of the depth of anesthesia in different stages: a comparative study. Tanaffos. 2009;8(2):46–53.Google Scholar
  4. Aziz W, Arif M. Multiscale permutation entropy of physiological time series. In: 9th International multitopic conference, IEEE INMIC 2005; 2005, IEEE.Google Scholar
  5. Bandt C. Ordinal time series analysis. Ecol Model. 2005;182(3):229–38.CrossRefGoogle Scholar
  6. Bandt C, Pompe B. Permutation entropy: a natural complexity measure for time series. Phys Rev Lett. 2002;88(17):174102.PubMedCrossRefGoogle Scholar
  7. Bell IR, et al. Nonlinear dynamical systems effects of homeopathic remedies on multiscale entropy and correlation dimension of slow wave sleep EEG in young adults with histories of coffee-induced insomnia. Homeopathy. 2012;101(3):182–92.PubMedPubMedCentralCrossRefGoogle Scholar
  8. Bezerianos A, Tong S, Thakor N. Time-dependent entropy estimation of EEG rhythm changes following brain ischemia. Ann Biomed Eng. 2003;31(2):221–32.PubMedCrossRefGoogle Scholar
  9. 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.PubMedCrossRefGoogle Scholar
  10. Bruhn J, et al. Shannon entropy applied to the measurement of the electroencephalographic effects of desflurane. Anesthesiology. 2001;95(1):30–5.PubMedCrossRefGoogle Scholar
  11. Bruhn J, et al. Depth of anaesthesia monitoring: what’s available, what’s validated and what’s next? Br J Anaesth. 2006;97(1):85–94.PubMedCrossRefGoogle Scholar
  12. Burton D, Zilberg E. Methods and apparatus for monitoring consciousness. 2002. wo patent wo/2002/100,267.Google Scholar
  13. Cao Y, et al. Detecting dynamical changes in time series using the permutation entropy. Phys Rev-Ser E. 2004;70(4; PART 2):46217–46217.Google Scholar
  14. Cao Y, et al. Characterization of complexity in the electroencephalograph activity of Alzheimer’s disease based on fuzzy entropy. Chaos. 2015;25(8):083116.PubMedCrossRefGoogle Scholar
  15. Chen Y, Yang H. Multiscale recurrence analysis of long-term nonlinear and nonstationary time series. Chaos, Solitons Fractals. 2012;45(7):978–87.CrossRefGoogle Scholar
  16. Chen W, et al. Characterization of surface EMG signal based on fuzzy entropy. Neural Syst Rehabil Eng, IEEE Trans. 2007;15(2):266–72.CrossRefGoogle Scholar
  17. Chen W, et al. Measuring complexity using FuzzyEn, ApEn, and SampEn. Med Eng Phys. 2009;31(1):61–8.PubMedCrossRefGoogle Scholar
  18. Chen D, et al. GPGPU-aided ensemble empirical-mode decomposition for EEG analysis during anesthesia. Inf Technol Biomed IEEE Trans. 2010;14(6):1417–27.CrossRefGoogle Scholar
  19. Costa M, Goldberger AL, Peng C-K. Multiscale entropy analysis of complex physiologic time series. Phys Rev Lett. 2002;89(6):068102.PubMedCrossRefGoogle Scholar
  20. Costa M, Goldberger AL, Peng C-K. Multiscale entropy analysis of biological signals. Phys Rev E. 2005;71(2):021906.CrossRefGoogle Scholar
  21. Escudero J, et al. Analysis of electroencephalograms in Alzheimer’s disease patients with multiscale entropy. Physiol Meas. 2006;27(11):1091.PubMedCrossRefGoogle Scholar
  22. He L, et al. Feature extraction with multiscale autoregression of multichannel time series for P300 speller BCI. In: Acoustics speech and signal processing (ICASSP), 2010 IEEE International Conference on. 2010, IEEE.Google Scholar
  23. Hsu W-Y, et al. Wavelet-based fractal features with active segment selection: application to single-trial EEG data. J Neurosci Methods. 2007;163(1):145–60.PubMedCrossRefGoogle Scholar
  24. Hu M, Liang H. Perceptual suppression revealed by adaptive multi-scale entropy analysis of local field potential in monkey visual cortex. Int J Neural Syst. 2013;23(2):1350005.PubMedCrossRefGoogle Scholar
  25. Huang NE, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc London, Ser A. 1998;454(1971):903–95.CrossRefGoogle Scholar
  26. Inouye T, et al. Quantification of EEG irregularity by use of the entropy of the power spectrum. Electroencephalogr Clin Neurophysiol. 1991;79(3):204–10.PubMedCrossRefGoogle Scholar
  27. Inuso G, et al. Brain activity investigation by EEG processing: wavelet analysis, kurtosis and Renyi’s entropy for artifact detection. In: Information acquisition. 2007. ICIA’07. International Conference on; 2007, IEEE.Google Scholar
  28. Jameson LC, Sloan TB. Using EEG to monitor anesthesia drug effects during surgery. J Clin Monit Comput. 2006;20(6):445–72.PubMedCrossRefGoogle Scholar
  29. Klockars JG, et al. 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.PubMedCrossRefGoogle Scholar
  30. Labate D, et al. Entropic measures of EEG complexity in Alzheimer’s disease through a multivariate multiscale approach. Sensors J, IEEE. 2013;13(9):3284–92.CrossRefGoogle Scholar
  31. Li X. Temporal structure of neuronal population oscillations with empirical model decomposition. Phys Lett A. 2006;356(3):237–41.CrossRefGoogle Scholar
  32. Li X, Ouyang G, Richards DA. Predictability analysis of absence seizures with permutation entropy. Epilepsy Res. 2007;77(1):70.PubMedCrossRefGoogle Scholar
  33. Li X, Cui S, Voss LJ. Using permutation entropy to measure the electroencephalographic effects of sevoflurane. Anesthesiology. 2008a;109(3):448.PubMedCrossRefGoogle Scholar
  34. Li X, et al. Analysis of depth of anesthesia with Hilbert–Huang spectral entropy. Clin Neurophysiol. 2008b;119(11):2465–75.PubMedCrossRefGoogle Scholar
  35. Li D, et al. Multiscale permutation entropy analysis of EEG recordings during sevoflurane anesthesia. J Neural Eng. 2010;7(4):046010.PubMedCrossRefGoogle Scholar
  36. Li D, et al. Parameter selection in permutation entropy for an electroencephalographic measure of isoflurane anesthetic drug effect. J Clin Monit Comput. 2012;27(2):113–23.PubMedCrossRefGoogle Scholar
  37. 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.PubMedCrossRefGoogle Scholar
  38. Liang Z, et al. EEG entropy measures in anesthesia. Front Comput Neurosci. 2015;9:16.PubMedPubMedCentralCrossRefGoogle Scholar
  39. Maszczyk T, Duch W. Comparison of Shannon, Renyi and Tsallis entropy used in decision trees. In: Artificial Intelligence and Soft Computing–ICAISC 2008. Springer; 2008. p. 643–51.Google Scholar
  40. McKay IDH, et al. Pharmacokinetic-pharmacodynamic modeling the hypnotic effect of sevoflurane using the spectral entropy of the electroencephalogram. Anesth Analg. 2006;102(1):91.PubMedCrossRefGoogle Scholar
  41. Monk TG, et al. Anesthetic management and one-year mortality after noncardiac surgery. Anesth Analg. 2005;100(1):4.PubMedCrossRefGoogle Scholar
  42. Montirosso R, et al. Infant’s emotional variability associated to interactive stressful situation: a novel analysis approach with Sample Entropy and Lempel–Ziv complexity. Infant Behav Dev. 2010;33(3):346–56.PubMedCrossRefGoogle Scholar
  43. Morabito FC, et al. Multivariate multi-scale permutation entropy for complexity analysis of Alzheimer’s disease EEG. Entropy. 2012;14(7):1186–202.CrossRefGoogle Scholar
  44. Natarajan K, et al. Nonlinear analysis of EEG signals at different mental states. Biomed Eng Online. 2004;3(1):7.PubMedPubMedCentralCrossRefGoogle Scholar
  45. Nunez PL, Wingeier BM, Silberstein RB. Spatial‐temporal structures of human alpha rhythms: theory, microcurrent sources, multiscale measurements, and global binding of local networks. Hum Brain Mapp. 2001;13(3):125–64.PubMedCrossRefGoogle Scholar
  46. Okogbaa OG, Shell RL, Filipusic D. On the investigation of the neurophysiological correlates of knowledge worker mental fatigue using the EEG signal. Appl Ergon. 1994;25(6):355–65.PubMedCrossRefGoogle Scholar
  47. Olofsen E, Sleigh J, Dahan A. Permutation entropy of the electroencephalogram: a measure of anaesthetic drug effect. Br J Anaesth. 2008;101(6):810–21.PubMedCrossRefGoogle Scholar
  48. Ouyang G, Dang C, Li X. Multiscale entropy analysis of EEG recordings in epileptic rats. Biomed Eng Appl Basis Commun. 2009;21(03):169–76.CrossRefGoogle Scholar
  49. Park J-H, et al. Multiscale entropy analysis of EEG from patients under different pathological conditions. Fractals. 2007;15(04):399–404.CrossRefGoogle Scholar
  50. Pincus SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci. 1991;88(6):2297.PubMedPubMedCentralCrossRefGoogle Scholar
  51. Rampil IJ. A primer for EEG signal processing in anesthesia. Anesthesiology. 1998;89(4):980–1002.PubMedCrossRefGoogle Scholar
  52. Renyi A. Probability theory. Amsterdam: North-Holland; 1970.Google Scholar
  53. Rezek I, Roberts SJ. Stochastic complexity measures for physiological signal analysis. Biomed Eng, IEEE Trans. 1998;45(9):1186–91.CrossRefGoogle Scholar
  54. 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.Google Scholar
  55. 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
  56. Rosso OA, et al. Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J Neurosci Methods. 2001;105(1):65–76.PubMedCrossRefGoogle Scholar
  57. Rosso O, Martin M, Plastino A. Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures. Physica A. 2003;320:497–511.CrossRefGoogle Scholar
  58. Rosso O, et al. EEG analysis using wavelet-based information tools. J Neurosci Methods. 2006;153(2):163–82.PubMedCrossRefGoogle Scholar
  59. Särkelä MOK, et al. Quantification of epileptiform electroencephalographic activity during sevoflurane mask induction. Anesthesiology. 2007;107(6):928–38.PubMedCrossRefGoogle Scholar
  60. Shalbaf R, et al. Using the Hilbert–Huang transform to measure the electroencephalographic effect of propofol. Physiol Meas. 2012;33(2):271–85.PubMedCrossRefGoogle Scholar
  61. Shannon CE. A mathematical theory of communication. ACM SIGMOBILE Mob Comput Commun Rev. 2001;5(1):3–55.CrossRefGoogle Scholar
  62. Shannon CE, Weaver W. The mathematical theory of communication. Urbana: University of Illinois Press; 1949, v (ie vii), 125 p.Google Scholar
  63. Smith WD, Dutton RC, Smith TN. Measuring the performance of anesthetic depth indicators. Anesthesiology. 1996;84(1):38–51.PubMedCrossRefGoogle Scholar
  64. Song Y, Zhang J. Discriminating preictal and interictal brain states in intracranial EEG by sample entropy and extreme learning machine. J Neurosci Methods. 2016;257:45–54.PubMedCrossRefGoogle Scholar
  65. Stamoulis C, Chang BS. Multiscale information for network characterization in epilepsy. In: Engineering in Medicine and Biology Society, EMBC, 2011 Annual international conference of the IEEE. 2011, IEEE.Google Scholar
  66. Takahashi T, et al. Antipsychotics reverse abnormal EEG complexity in drug-naive schizophrenia: a multiscale entropy analysis. Neuroimage. 2010;51(1):173–82.PubMedPubMedCentralCrossRefGoogle Scholar
  67. Thuraisingham RA, Gottwald GA. On multiscale entropy analysis for physiological data. Physica A. 2006;366:323–32.CrossRefGoogle Scholar
  68. Tong S, et al. Parameterized entropy analysis of EEG following hypoxic–ischemic brain injury. Phys Lett A. 2003;314(5):354–61.CrossRefGoogle Scholar
  69. Tsallis C, Mendes R, Plastino AR. The role of constraints within generalized nonextensive statistics. Physica A. 1998;261(3):534–54.CrossRefGoogle Scholar
  70. Unser M, Aldroubi A. A review of wavelets in biomedical applications. Proc IEEE. 1996;84(4):626–38.CrossRefGoogle Scholar
  71. Viertiö‐Oja H, et al. Description of the Entropy™ algorithm as applied in the Datex‐Ohmeda S/5™ Entropy module. Acta Anaesthesiol Scand. 2004;48(2):154–61.PubMedCrossRefGoogle Scholar
  72. Wang Y, et al. Multi-scale sample entropy of electroencephalography during sevoflurane anesthesia. J Clin Monit Comput. 2014;28(4):409–17.PubMedCrossRefGoogle Scholar
  73. Wu S-D, et al. Modified multiscale entropy for short-term time series analysis. Physica A. 2013;392(23):5865–73.CrossRefGoogle Scholar
  74. Yoo CS, et al. Automatic detection of seizure termination during electroconvulsive therapy using sample entropy of the electroencephalogram. Psychiatry Res. 2012;195(1):76–82.PubMedCrossRefGoogle Scholar
  75. Yoon YG, et al. Monitoring the depth of anesthesia from rat EEG using modified Shannon entropy analysis. Conf Proc IEEE Eng Med Biol Soc. 2011;2011:4386–9.PubMedGoogle Scholar
  76. Zadeh LA. Fuzzy sets. Inf Control. 1965;8(3):338–53.CrossRefGoogle Scholar
  77. Zandi AS, et al. An entropy-based approach to predict seizures in temporal lobe epilepsy using scalp EEG. Conf Proc IEEE Eng Med Biol Soc. 2009;2009:228–31.PubMedGoogle Scholar
  78. Zandi AS, et al. Circadian variation of scalp EEG: a novel measure based on wavelet packet transform and differential entropy. Conf Proc IEEE Eng Med Biol Soc. 2013;2013:6297–300.PubMedGoogle Scholar
  79. Zhang R, et al. Predicting inter-session performance of SMR-based brain-computer interface using the spectral entropy of resting-state EEG. Brain Topogr. 2015;28(5):680–90.PubMedCrossRefGoogle Scholar
  80. Zhaohui L, Xiaoli L. Estimating temporal causal interaction between spike trains with permutation and transfer entropy. Plos One. 2013;8(8):e70894.CrossRefGoogle Scholar
  81. Zou X, Lei M. Pattern recognition of surface electromyography signal based on multi-scale fuzzy entropy. Sheng Wu Yi Xue Gong Cheng Xue Za Zhi. 2012;29(6):1184–8.PubMedGoogle Scholar
  82. Zoughi T, Boostani R, Deypir M. A wavelet-based estimating depth of anesthesia. Eng Appl Artif Intell. 2012;25(8):1710–22.CrossRefGoogle Scholar
  83. Zunino L, et al. Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy. Physica A. 2008;387(24):6057–68.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Institute of Electric EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.Key Laboratory of Industrial Computer Control Engineering of Hebei ProvinceYanshan UniversityQinhuangdaoChina
  3. 3.State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain ResearchBeijing Normal UniversityBeijingChina
  4. 4.Center for Collaboration and Innovation in Brain and Learning SciencesBeijing Normal UniversityBeijingChina

Personalised recommendations