New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake
- 51 Downloads
A number of measures, stemming from nonlinear dynamics, exist to estimate complexity of biomedical objects. In most cases they are appropriate, but sometimes unconventional measures, more suited for specific objects, are needed to perform the task. In our present work, we propose three new complexity measures to quantify complexity of topographic closed loops of alpha carrier frequency phase potentials (CFPP) of healthy humans in wake and drowsy states. EEG of ten adult individuals was recorded in both states, using a 14-channel montage. For each subject and each state, a topographic loop (circular directed graph) was constructed according to CFPP values. Circular complexity measure was obtained by summing angles which directed graph edges (arrows) form with the topographic center. Longitudinal complexity was defined as the sum of all arrow lengths, while intersecting complexity was introduced by counting the number of intersections of graph edges. Wilcoxon’s signed-ranks test was used on the sets of these three measures, as well as on fractal dimension values of some loop properties, to test differences between loops obtained in wake vs. drowsy. While fractal dimension values were not significantly different, longitudinal and intersecting complexities, as well as anticlockwise circularity, were significantly increased in drowsy.
KeywordsAlpha activity Phase potentials Wake and drowsy Circular graphs Complexity
We express our gratitude to the Institute for Mental Health, Belgrade, where part of this work was done, as well as to all participants in the experiments.
This work was financed by the Ministry of Education, Science and Technological Development of the Republic of Serbia (projects OI 173022 and III 41028).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 3.Berwanger D, Grädel E (2005) Entanglement—a measure for the complexity of directed graphs with applications to logic and games. In: Baader F, Voronkov A (eds) Volume 3452 of the series Lecture Notes in Computer Science. Springer, Berlin, pp 209–223Google Scholar
- 5.Boly M, Phillips C, Tshibanda L, Vanhaudenhuyse A, Schabus M, Dang-Vu TT, Moonen G, Hustinx R, Maquet P, Laureys S (2008) Intrinsic brain activity in altered states of consciousness: how conscious is the default mode of brain function? Ann N Y Acad Sci 1129(1):119–129CrossRefPubMedPubMedCentralGoogle Scholar
- 22.Ma Y, Shi W, Peng C-K, Yang AC (2017) Nonlinear dynamical analysis of sleep electroencephalography using fractal and entropy approaches. Sleep Med Rev. https://doi.org/10.1016/j.smrv.2017.01.003
- 28.Petrosian A (1995) Kolmogorov complexity of finite sequences and recognition of different preictal EEG patterns, In: Computer-based medical systems, Proceedings of the Eighth IEEE Symposium on; IEEE, pp 212–217Google Scholar
- 31.Rezaei SSC (2013) Entropy and graphs, master thesis, University of Waterloo, Waterloo, Ontario, https://arxiv.org/pdf/1311.5632.pdf, Accessed 25 Aug 2017
- 36.Vinck M, Oostenveld R, van Wingerden M, Battaglia F, Pennartz CMA (2011) An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. NeuroImage 55:1548–1565. https://doi.org/10.1016/j.neuroimage.2011.01.055 CrossRefPubMedGoogle Scholar
- 38.Weiss B, Clemens Z, Bódizs R, Halász P (2011) Comparison of fractal and power spectral EEG features: effects of topography and sleep stages. Brain Res Bull 84:359–375. https://doi.org/10.1016/j.brainresbull.2010.12.005 CrossRefPubMedGoogle Scholar