Abstract
Increasing evidences show that multiscale complexity measure is an intuitive and effective measure in quantifying various physical and physiological states. In this study, we demonstrate that the classical algorithm of multiscale Lempel–Ziv complexity (multiscale LZC or MLZ) has a critical limitation in neglecting rapid rhythms in complex systems. To this end, simulations added with different levels of white noise are designed to examine whether or not MLZ calculation neglects the effects of high-frequency noise. In addition, an algorithm by obtaining coarse-grained multiscale LZC, so-called generalized multiscale LZC (gMLZ), is proposed to yield a spectrum of complexity. A series of simulated non-stationary signals are generated for comparing the performances between MLZ and gMLZ. Besides, cyclic alternating pattern (CAP), characterized by the excessive synchronization of neuronal activity, has been associated with its power and physiological states. To understand how the synchronization of neuronal activities in different phase-A subtypes in exerting an influence over its power and complexity, we analyze the gMLZ of the real CAP database and compare it to its power spectra as well as modified multiscale entropy (MMSE), which is one of the most well-known multiscale complexity-based measures. The novel algorithm reveals that the evaluated complexities in different phase-A subtypes are inversely related to both the power and excessive synchronization in different timescales in general. The impact of frequencies, sleep stages and pathophysiological conditions on these two complexity measures is also examined. The discerning abilities of different phase-A subtypes using coarse-grained complexity measures (gMLZ and MMSE) are more consistent than power across different time scales. Our approach makes up a deficiency in handling with high-frequency oscillations and enables us to examine complexities of nonlinear systems in a wide-range of timescales.
Similar content being viewed by others
References
Costa, M., Goldberger, A.L., Peng, C.K.: Multiscale entropy analysis of biological signals. Phys. Rev. E 71, 021906 (2005)
Stam, C.J.: Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin. Neurophysiol. 116, 2266–2301 (2005)
Kolmogorov, A.N.: Three approaches to the definition of the concept “quantity of information”. Probl. Peredachi Inf. 1, 3–11 (1965)
Solomonoff, R.J.: A formal theory of inductive inference. Part II. Inf. Control 7, 224–254 (1964)
Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Inf. Theory 22, 75–81 (1976)
Kaspar, F., Schuter, H.G.: Easily calculable measure for the complexity of spatiotemporal patterns. Phys. Rev. A 36, 842–848 (1987)
Jeong, J., Chae, J.H., Kim, S.Y., Han, S.H.: Nonlinear dynamic analysis of the EEG in patients with Alzheimer’s disease and vascular dementia. Clin. Neurophysiol. 18, 58–67 (2001)
Jeong, J., Kim, S.Y., Han, S.H.: Non-linear dynamical analysis of the EEG in Alzheimer’s disease with optimal embedding dimension. Electroen. Clin. Neurophysio 106, 220–228 (1998)
Jelles, B., van Birgelen, J.H., Slaets, J.P., Hekster, R.E., Jonkman, E.J., Stam, C.J.: Decrease of non-linear structure in the EEG of Alzheimer patients compared to healthy controls. Clin. Neurophysiol. 110, 1159–1167 (1999)
Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346 (1983)
Eckmann, J.P., Ruelle, D.: Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D 56, 185–187 (1992)
Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Psychol. 278, H2039–H2049 (2000)
Nagaragan, R.: Quantifying physiological data with Lempel-Ziv complexity-certain issues. IEEE T. Biomed. Eng. 49, 1371–1373 (2002)
Aboy, M., Hornero, R., Abásolo, D., Alvarez, D.: Interpretation of the Lempel-Ziv complexity measure in the context of biomedical signal analysis. IEEE T. Biomed. Eng. 53, 2282–2288 (2006)
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. 119, 1232–1241 (2008)
Fernández, A., López-Ibor, M.I., Turrero, A., Santos, J.M., Morón, M.D., Hornero, R., Gómez, C., Méndez, M.A., Ortiz, T., López-Ibor, J.J.: Lempel-Ziv complexity in schizophrenia: a MEG study. Clin. Neurophysiol. 122, 2227–2235 (2011)
Fernández, A., Zuluaga, P., Abásolo, D., Gómez, C., Serra, A., Méndez, M.A., Hornero, R.: Brain oscillatory complexity across the life span. Clin. Neurophysiol. 123, 2154–2162 (2012)
Hornero, R., Abásolo, D., Escudero, J., Gómez, C.: Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer’s disease. Philos. Trans. R. Soc. A 367, 317–336 (2009)
Dauwels, J., Srinivasan, K., Ramasubba Reddy, M., Musha, T., Vialatte, F.B., 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, 539621 (2011)
Jouny, C.C., Bergey, C.K.: Characterization of early partial seizure onset: frequency, complexity and entropy. Clin. Neurophysiol. 123, 658–669 (2012)
Niedermeyer, E.: The normal EEG in the waking adult.Electroencephalography: Basic Principles, Clinical Applications, and Related field. Williams & Wilkins, Baltimore (1999)
Buzsáki, G., Draguhn, A.: Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004)
Sanei, S., Chambers, J.: Introduction in EEG. Wiley, New York (2007)
Goldberger, A.L., Amaral, L.A., Hausdorff, J.M., Ivanov, PCh., Peng, C.K., Stanley, H.E.: Fractal dynamics in physiology: alterations with disease and aging. Proc. Natl. Acad. Sci. USA 99, 2466–2472 (2002)
Ibáñez-Molina, A.J., Iglesias-Parro, S., Soriano, M.F., Aznarte, J.I.: Multiscale Lempel-Ziv complexity for EEG measures. Clin. Neurophysiol. 126, 541–548 (2015)
Hu, J., Gao, J., Wang, X.: Multifractal analysis of sunspot time series: the effects of the 11-year cycle and Fourier truncation. J. Stat. Mech. C Theory Exp. 2, P02066 (2009)
Bell, I.R., Howerter, A., Jackson, N., Aickin, M., Bootzin, R.R., Brooks, A.J.: 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 101, 182–192 (2012)
Chung, C.C., Kang, J.H., Yuan, R.Y., Wu, D., Chen, C.C., Chi, N.F., Chen, P.C., Hu, C.J.: Multiscale entropy analysis of electroencephalography during sleep in patient with Parkinson disease. Clin. EEG Neurosci. 44, 221–226 (2013)
Shi, W., Shang, P., Ma, Y., Sun, S., Yeh, C.H.: A comparison study on stages of sleep: Quantifying multiscale complexity using higher moments on coarse-graining. Commun. Nonlinear Sci. Numer. Simul. 44, 292–303 (2017)
Humeau-Heurtier, A.: The multiscale entropy algorithm and its variants: a review. Entropy 17, 3110–3123 (2015)
Wu, S.D., Wu, C.W., Lee, K.Y., Lin, S.G.: Modified multiscale entropy for short-term time series analysis. Phys. A. 392, 5865–5873 (2013)
Terzano, M.G., Mancia, D., Salati, M.R., Costani, G., Decembrino, A., Parrino, L.: The cyclic alternating pattern as a physiologic component of normal NREM sleep. Sleep 8, 137–145 (1985)
Terzano, M.G., Parrino, L., Sherieri, A., Chervin, R., Chokroverty, S., Guilleminault, C., Hirshkowitz, M., Mahowald, M., Moldofsky, H., Rosa, A., Thomas, R., Walters, A.: Atlas, rules, and recording techniques for the scoring of cyclic alternating pattern (CAP) in human sleep. Sleep Med. 2, 537–553 (2001)
Lundberg, N.: Continuous recording and control of ventricular fluid pressure in neurosurgical practice. Acta. Psychiatr. Scand. 36, 1–193 (1960)
Evans, B.M.: Periodic activity in cerebral arousal mechanisms-the relationship to sleep and brain damage. Electroencephalogr. Clin. Neurophysiol. 83, 130–137 (1992)
Steriade, M., Amzica, F., Contreras, D.: Cortical and thalamic cellular correlates of electroencephalographic burst-suppression. Electroencephalogr. Clin. Neurophysiol. 90, 1–16 (1994)
Goldberger, A.L., Amaral, L.A., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101, e215–e220 (2000)
Rechtscahffen, A.: A manual of standardized terminology, techniques and scoring system for sleep stages of human subjects. U.S. National Institutes of Health 204 (1968)
De Carli, F., Nobili, L., Beelke, M., Watanabe, T., Smerieri, A., Parrino, L., Terzano, M.G., Ferrillo, F.: Quantitative analysis of sleep EEG microstructure in the time-frequency domain. Brain Res. Bull. 63, 399–405 (2004)
Ferri, R., Rundo, F., Bruni, O., Terzano, M.G., Stam, C.J.: Dynamics of the EEG slow-wave synchronization during sleep. Clin. Neurophysiol. 116, 2783–2795 (2005)
Togo, F., Cherniack, N.S., Natelson, B.H.: Electroencephalogram characteristics of autonomic arousals during sleep in healthy men. Clin. Neurophysiol. 117, 2597–2603 (2006)
Ferri, R., Parrino, L., Smerieri, A., Terzano, M.G., Elia, M., Musumeci, S.A., Pettinato, S.J.: Cyclic alternating pattern and spectral analysis of heart rate variability during normal sleep. Sleep Res. 9, 13–18 (2000)
Ferri, R., Bruni, O., Miano, S., Terzano, M.G.: Topographic mapping of the spectral components of the cyclic alternating pattern (CAP). Sleep Med. 6, 29–36 (2005)
Terzano, M.G., Parrino, L., Boselli, M., Smerieri, A., Spaggiari, M.C.: CAP components and EEG synchronization in the first 3 sleep cycles. Clin. Neurophysiol. 111, 283–290 (2000)
Ferrillo, F., Gabarra, M., Nobili, L., Parrino, L., Schiavi, G., Stubinski, B., Terzano, M.G.: Comparison between visual scoring of cyclic alternating pattern (CAP) and computerized assessment of slow EEG oscillations in the transition from light to deep non-REM sleep. J. Clin. Neurophysiol. 14, 210–216 (1997)
Stam, C.J., Nicolai, J., Keunen, R.W.: Nonlinear dynamical analysis of periodic lateralized epileptiform discharges. Clin. Electroencephalogr. 29, 101–105 (1998)
Ferri, R., Parrino, L., Smerieri, A., Terzano, M.G., Elia, M., Musumeci, S.A., Pettinato, S., Stam, C.J.: Non-linear EEG measures during sleep: effects of the different sleep stages and cyclic alternating pattern. Int. J. Psychophysiol. 43, 273–286 (2002)
Acknowledgements
This research is sponsored by the China Postdoctoral Science Foundation (Grant 043206005).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Yeh, CH., Shi, W. Generalized multiscale Lempel–Ziv complexity of cyclic alternating pattern during sleep. Nonlinear Dyn 93, 1899–1910 (2018). https://doi.org/10.1007/s11071-018-4296-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-018-4296-9