Effect of linear mixing in EEG on synchronization and complex network measures studied using the Kuramoto model. (English) Zbl 1514.92048
Summary: Volume conduction in the brain may influence the synchronization between EEG signals considerably, as it may lead to detection of spurious functional couplings among the recording channels. It has been shown that the volume conduction effect can be approximated as a linear mixing of the electrical fields of the brain regions. In this paper, we investigate the reliability of various synchronization measures in the presence of the linear superposition in EEG time series. For this purpose, we applied linear mixing to artificially generated EEG times series using the Kuramoto model of coupled phase oscillators, which represents the behavior of coupled systems with local interactions at the fundamental level. Our simulation results showed that the phase-lag index and the synchronization measures based on the visibility graph algorithms were less sensitive to the linear mixing effect and could predict the coupling degree correctly even with strongly overlapping signals. The results of our further data analyses demonstrated the effect of linear superposition in time series on the behavior of various complex network measures. For each case, we provide recommendations for proper choices of synchronization measures to obtain complex network characteristics that are minimally sensitive to linear mixing.
MSC:
| 92C55 | Biomedical imaging and signal processing |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
Software:
FieldTripReferences:
| [1] | Bullmore, E.; Sporns, O., Complex brain networks: graph theoretical analysis of structural and functional systems, Nat. Rev. Neurosci., 10, 3, 186-198 (2009) |
| [2] | Bullmore, E.; Sporns, O., The economy of brain network organization, Nat. Rev. Neurosci., 13, 5, 336-349 (2012) |
| [3] | Ariely, D.; Berns, G. S., Neuromarketing: the hope and hype of neuroimaging in business, Nat. Rev. Neurosci., 11, 4, 284-292 (2010) |
| [4] | He, Y.; Evans, A., Graph theoretical modeling of brain connectivity, Curr. Opin. Neurol., 23, 4, 341-350 (2010) |
| [5] | Rubinov, M.; Sporns, O., Complex network measures of brain connectivity: uses and interpretations, Neuroimage, 52, 3, 1059-1069 (2010) |
| [6] | Bullmore, E. T.; Bassett, D. S., Brain graphs: graphical models of the human brain connectome, Annu. Rev. Clin. Psychol., 7, 113-140 (2011) |
| [7] | König, T.; Prichep, L.; Dierks, T.; Hubl, D.; Wahlund, L.; John, E.; Jelic, V., Decreased eeg synchronization in alzheimer’s disease and mild cognitive impairment, Neurobiol. Aging, 26, 2, 165-171 (2005) |
| [8] | Nunez, P.; Silberstein, R.; Cadusch, P.; Wijesinghe, R.; Westdorp, A.; Srinivasan, R., A theoretical and experimental study of high resolution eeg based on surface laplacians and cortical imaging, Electroencephalogr. Clin. Neurophysiol., 90, 1, 40-57 (1994) |
| [9] | He, B.; Yang, L.; Wilke, C.; Yuan, H., Electrophysiological imaging of brain activity and connectivity challenges and opportunities, IEEE Trans. Biomed. Eng., 58, 7, 1918-1931 (2011) |
| [10] | Srinivasan, R.; Nunez, P. L.; Tucker, D. M.; Silberstein, R. B.; Cadusch, P. J., Spatial sampling and filtering of EEG with spline laplacians to estimate cortical potentials, Brain Topogr., 8, 4, 355-366 (1996) |
| [11] | Makeig, S.; Bell, A. J.; Jung, T. P.; Sejnowski, T. J., Independent component analysis of electroencephalographic data, (Advances in neural information processing systems (1996)), 145-151 |
| [12] | Nunez, P. L.; Srinivasan, R.; Westdorp, A. F.; Wijesinghe, R. S.; Tucker, D. M.; Silberstein, R. B.; Cadusch, P. J., Eeg coherency: i: statistics, reference electrode, volume conduction, laplacians, cortical imaging, and interpretation at multiple scales, Electroencephalogr. Clin. Neurophysiol., 103, 5, 499-515 (1997) |
| [13] | Schoffelen, J.-M.; Gross, J., Source connectivity analysis with MEG and EEG, Hum. Brain Mapp., 30, 6, 1857-1865 (2009) |
| [14] | Srinivasan, R.; Nunez, P. L.; Silberstein, R. B., Spatial filtering and neocortical dynamics: estimates of eeg coherence, IEEE Trans. Biomed. Eng., 45, 7, 814-826 (1998) |
| [15] | Nunez, P. L.; Srinivasan, R., Electric Fields of the Brain: the Neurophysics of EEG (2006), Oxford University Press: Oxford University Press USA |
| [16] | Kuramoto, Y., Chemical Oscillations, Waves, and Turbulence, vol. 19 (2012), Springer Science & Business Media · Zbl 0558.76051 |
| [17] | Kiss, I. Z.; Zhai, Y.; Hudson, J. L., Emerging coherence in a population of chemical oscillators, Science, 296, 5573, 1676-1678 (2002) |
| [18] | Peraza, L. R.; Asghar, A. U.; Green, G.; Halliday, D. M., Volume conduction effects in brain network inference from electroencephalographic recordings using phase lag index, J. Neurosci. Methods, 207, 2, 189-199 (2012) |
| [19] | Stam, C. J.; Nolte, G.; Daffertshofer, A., Phase lag index: assessment of functional connectivity from multi channel eeg and meg with diminished bias from common sources, Hum. Brain Mapp., 28, 11, 1178-1193 (2007) |
| [20] | Lobier, M.; Siebenhühner, F.; Palva, S.; Palva, J. M., Phase transfer entropy: a novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions, Neuroimage, 85, 853-872 (2014) |
| [21] | Oostenveld, R.; Fries, P.; Maris, E.; Schoffelen, J.-M., Fieldtrip: open source software for advanced analysis of meg, eeg, and invasive electrophysiological data, Comput. Intell. Neurosci., 2011, 1 (2011) |
| [22] | Yu, M.; Hillebrand, A.; Gouw, A. A.; Stam, C. J., Horizontal visibility graph transfer entropy (hvg-te): a novel metric to characterize directed connectivity in large-scale brain networks, NeuroImage (2017) |
| [23] | Ahmadi, N.; Carrette, E.; Aldenkamp, A. P.; Pechenizkiy, M., Finding predictive EEG complexity features for classification of epileptic and psychogenic nonepileptic seizures using imperialist competitive algorithm, (2018 IEEE 31st International Symposium on Computer-Based Medical Systems (CBMS) (2018), IEEE), 164-169 |
| [24] | Box, G. E.; Jenkins, G. M.; Reinsel, G. C.; Ljung, G. M., Time Series Analysis: Forecasting and Control (2015), John Wiley & Sons |
| [25] | Gabor, D., Theory of communication. part 1: the analysis of information, J. Inst. Electr. Eng., 93, 26, 429-441 (1946) |
| [26] | Nolte, G.; Bai, O.; Wheaton, L.; Mari, Z.; Vorbach, S.; Hallett, M., Identifying true brain interaction from eeg data using the imaginary part of coherency, Clin. Neurophysiol., 115, 10, 2292-2307 (2004) |
| [27] | Mormann, F.; Lehnertz, K.; David, P.; Elger, C. E., Mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients, Physica D, 144, 3-4, 358-369 (2000) · Zbl 0962.92020 |
| [28] | Stam, C.; Van Dijk, B., Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets, Physica D, 163, 3, 236-251 (2002) · Zbl 0986.37074 |
| [29] | Montez, T.; Linkenkaer-Hansen, K.; Van Dijk, B.; Stam, C., Synchronization likelihood with explicit time-frequency priors, Neuroimage, 33, 4, 1117-1125 (2006) |
| [30] | Betzel, R. F.; Erickson, M. A.; Abell, M.; O’Donnell, B. F.; Hetrick, W. P.; Sporns, O., Synchronization dynamics and evidence for a repertoire of network states in resting eeg, Front. Comput. Neurosci., 6, 74 (2012) |
| [31] | Lacasa, L.; Toral, R., Description of stochastic and chaotic series using visibility graphs, Phys. Rev. E, 82, 3, 036120 (2010) |
| [32] | Luque, B.; Lacasa, L.; Ballesteros, F.; Luque, J., Horizontal visibility graphs: exact results for random time series, Phys. Rev. E, 80, 4, 046103 (2009) |
| [33] | Campanharo, A. S.; Sirer, M. I.; Malmgren, R. D.; Ramos, F. M.; Amaral, L. A.N., Duality between time series and networks, PLoS One, 6, 8, Article e23378 pp. (2011) |
| [34] | Ahmadlou, M.; Adeli, H., Visibility graph similarity: a new measure of generalized synchronization in coupled dynamic systems, Physica D, 241, 4, 326-332 (2012) |
| [35] | Ahmadi, N.; Pechenizkiy, M., Application of horizontal visibility graph as a robust measure of neurophysiological signals synchrony, (Computer-Based Medical Systems (CBMS), 2016 IEEE 29th International Symposium on (2016), IEEE), 273-278 |
| [36] | Antoniou, I.; Tsompa, E., Statistical analysis of weighted networks, Discrete Dyn. Nat. Soc., 2008 (2008) · Zbl 1159.90315 |
| [37] | Costa, L.d. F.; Rodrigues, F. A.; Travieso, G.; Villas Boas, P. R., Characterization of complex networks: a survey of measurements, Adv. Phys., 56, 1, 167-242 (2007) |
| [38] | Brandes, U.; Pich, C., Centrality estimation in large networks, Int. J. Bifurcation Chaos, 17, 07, 2303-2318 (2007) · Zbl 1143.05304 |
| [39] | Van Mieghem, P., Graph Spectra for Complex Networks (2010), Cambridge University Press |
| [40] | Lohmann, G.; Margulies, D. S.; Horstmann, A.; Pleger, B.; Lepsien, J.; Goldhahn, D.; Schloegl, H.; Stumvoll, M.; Villringer, A.; Turner, R., Eigenvector centrality mapping for analyzing connectivity patterns in fmri data of the human brain, PLoS One, 5, 4, Article e10232 pp. (2010) |
| [41] | Manrubia, S. C.; Mikhailov, A. S., Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems (2004), World Scientific · Zbl 1119.34001 |
| [42] | Haken, H., Brain dynamics(synchronisation and activity patterns in pulse-coupled neural nets with delays and noise), (Springer Series in Synergetics (2002), Springer) · Zbl 1082.92014 |
| [43] | Ermentrout, G.; Kopell, N., Parabolic bursting in an excitable system coupled with a slow oscillation, SIAM J. Appl. Math., 46, 2, 233-253 (1986) · Zbl 0594.58033 |
| [44] | Ermentrout, G.; Kopell, N., Oscillator death in systems of coupled neural oscillators, SIAM J. Appl. Math., 50, 1, 125-146 (1990) · Zbl 0686.34033 |
| [45] | Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42 (2013), Springer Science & Business Media |
| [46] | Brown, E.; Moehlis, J.; Holmes, P., On the phase reduction and response dynamics of neural oscillator populations, Neural Comput., 16, 4, 673-715 (2004) · Zbl 1054.92006 |
| [47] | Breakspear, M.; Heitmann, S.; Daffertshofer, A., Generative models of cortical oscillations: neurobiological implications of the kuramoto model, Front. Hum. Neurosci., 4, 190 (2010) |
| [48] | Kandel, E. R.; Schwartz, J. H.; Jessell, T. M.; Siegelbaum, S. A.; Hudspeth, A. J., Principles of Neural Science, vol. 4 (2000), McGraw-hill: McGraw-hill New York |
| [49] | Llinás, R. R., The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function, Science, 242, 4886, 1654-1664 (1988) |
| [50] | Hutcheon, B.; Yarom, Y., Resonance, oscillation and the intrinsic frequency preferences of neurons, Trends Neurosci., 23, 5, 216-222 (2000) |
| [51] | Gómez-Gardeñes, J.; Zamora-López, G.; Moreno, Y.; Arenas, A., From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex, PloS One, 5, 8, Article e12313 pp. (2010) |
| [52] | Pereda, E.; Quiroga, R. Q.; Bhattacharya, J., Nonlinear multivariate analysis of neurophysiological signals, Prog. Neurobiol., 77, 1, 1-37 (2005) |
| [53] | Alonso, J.-M.; Usrey, W. M.; Reid, R. C., Precisely correlated firing in cells of the lateral geniculate nucleus, Nature, 383, 6603, 815 (1996) |
| [54] | Simpson, D.; Infantosi, A.; Rosas, D. B., Estimation and significance testing of cross-correlation between cerebral blood flow velocity and background electro-encephalograph activity in signals with missing samples, Med. Biol. Eng. Comput., 39, 4, 428-433 (2001) |
| [55] | Lachaux, J. P.; Rodriguez, E.; Martinerie, J.; Varela, F. J., Measuring phase synchrony in brain signals, Hum. brain Mapp., 8, 4, 194-208 (1999) |
| [56] | Varela, F.; Lachaux, J. P.; Rodriguez, E.; Martinerie, J., The brainweb: phase synchronization and large-scale integration, Nat. Rev. Neurosci., 2, 4, 229 (2001) |
| [57] | Bowyer, S. M., Coherence a measure of the brain networks: past and present, Neuropsych. Electrophys., 2, 1, 1 (2016) |
| [58] | Domínguez, L. G.; Stieben, J.; Velázquez, J. L.P.; Shanker, S., The imaginary part of coherency in autism: differences in cortical functional connectivity in preschool children, PLoS One, 8, 10, Article e75941 pp. (2013) |
| [59] | González, G.; Van der Molen, M.; Žarić, G.; Bonte, M.; Tijms, J.; Blomert, L.; Stam, C.; Van der Molen, M., Graph analysis of eeg resting state functional networks in dyslexic readers, Clin. Neurophysiol., 127, 9, 3165-3175 (2016) |
| [60] | Vinck, M.; Oostenveld, R.; Van Wingerden, M.; Battaglia, F.; Pennartz, C. M., An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias, Neuroimage, 55, 4, 1548-1565 (2011) |
| [61] | Pikovsky, A.; Rosenblum, M.; Kurths, J.; Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences, vol. 12 (2003), Cambridge university press · Zbl 1219.37002 |
| [62] | Lacasa, L.; Luque, B.; Ballesteros, F.; Luque, J.; Nuno, J. C., From time series to complex networks: the visibility graph, Proc. Natl. Acad. Sci., 105, 13, 4972-4975 (2008) · Zbl 1205.05162 |
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