Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T02:40:48.823Z Has data issue: false hasContentIssue false

9 - State space representation and global descriptors of brain electrical activity

Published online by Cambridge University Press:  15 December 2009

By
Jiří Wackermann  and
Carsten Allefeld
Edited by
Christoph M. Michel ,
Thomas Koenig ,
Daniel Brandeis ,
Lorena R. R. Gianotti  and
Jiří Wackermann
Christoph M. Michel
Affiliation:
Université de Genève
Thomas Koenig
Affiliation:
University Hospital of Psychiatry, Berne, Switzerland
Daniel Brandeis
Affiliation:
Department of Child and Adolescent Psychiatry, University of Zurich, Switzerland and Central Institute of Mental Health, Mannheim, Grmany
Lorena R. R. Gianotti
Affiliation:
Universität Zürich
Jiří Wackermann
Affiliation:
Institute for Frontier Areas of Psychology and Mental Health, Freiburg im Breisgau, Germany
Get access

Summary

The methods introduced in this chapter aim at a comprehensive assessment of the brain's functional state via a small number of “global” quantitative descriptors. Unlike the approaches presented in the preceding chapters, the objective of the global approach is not a mapping of the brain's functions within the real (physical) three-dimensional space, but rather a mapping of the variety of the brain's functional states into an abstract (mathematical) multidimensional space. Nevertheless, the global methodology shares with the other methods the focus on the spatial configuration of brain electrical fields, is closely related to microstate analysis, and as such belongs in the context of functional brain topography and electrical neuroimaging.

The state space representation

The notion of state space

The state, or temporary condition, of a given system is characterized by observations, usually in the form of measurements. For example, the weather situation at a given place and time may be assessed by measuring the temperature θ, the relative humidity h and the air pressure p. A convenient representation of the momentary state, which is characterized by three quantities, is a single point within a three-dimensional state space, located at coordinates (θ, h, p). The state space representation is useful in many cases because it gives an overview over all possible states of the system at once. Moreover, the evolution of the state over time appears as a movement within this space, or, disregarding time measure, as a path consisting of successive state points, the state space trajectory.

Type
Chapter
Information
Electrical Neuroimaging , pp. 191 - 214
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allefeld, C, H, Atmanspacher, Wackermann, J.Mental states as macrostates emerging from EEG dynamics. Chaos 2009;19 in press.CrossRefGoogle Scholar
Lehmann, D, Skrandies, W. Reference-free identification of components of checkerboard-evoked multichannel potential fields. Electroencephalography and Clinical Neurophysiology 1980;48:609–621.CrossRefGoogle ScholarPubMed
Lehmann, D.Principles of spatial analysis. In Gevins, AS, Rémond, A, eds. Methods of Analysis of Brain Electrical and Magnetic Signals. Amsterdam: Elsevier; 1987, pp. 309–354.Google Scholar
Brandeis, D, Naylor, H, Halliday, R, Callaway, E, Yano, L.Scopolamine effects on visual information processing, attention and event-related potential map latencies. Psychophysiology 1992;29:315–336.CrossRefGoogle ScholarPubMed
Jolliffe, IT. Principal Component Analysis. 2nd edn. New York: Springer; 2002.Google Scholar
Golub, GH, Loan, CF. Matrix Computations. Baltimore: John Hopkins University Press; 1983.Google Scholar
Lehmann, D. Multichannel topography of human alpha EEG fields. Electroencephalography and Clinical Neurophysiology 1971;31:439–449.CrossRefGoogle ScholarPubMed
Silberstein, R, Cadusch, PJ, Schier, MA. Volume conduction effects on spatial principal components analysis of scalp recorded brain electrical activity. Brain Topography 1990;3:273–274.Google Scholar
Wackermann, J, Allefeld, C. On the meaning and interpretation of global descriptors of brain electrical activity. Including a reply to X. Pei et al. International Journal of Psychophysiology 2007;64:199–210.CrossRefGoogle Scholar
Wackermann, J. Beyond mapping: estimating complexity of multichannel EEG recordings. Acta Neurobiologiae Experimentalis 1996;56:197–208.Google ScholarPubMed
Hjorth, B. EEG analysis based on time domain properties. Electroencephalography and Clinical Neurophysiology 1970;29:306–310.CrossRefGoogle ScholarPubMed
Hjorth, B. The physical significance of the time domain descriptors in EEG analysis. Electroencephalography and Clinical Neurophysiology 1973;34:321–325.CrossRefGoogle ScholarPubMed
Paluš, M, Dvořák, I, David, I.Remarks on spatial and temporal dynamics of EEG. In Dvořák, I, Holden, AV, eds. Mathematical Approaches to Brain Functioning Diagnostics. Manchester: Manchester University Press; 1991, pp. 369–385.Google Scholar
Pézard, L, Nandrino, JL, Renault, Bet al. Depression as a dynamical disease. Biological Psychiatry 1996;39:991–999.CrossRefGoogle ScholarPubMed
James, CJ, Lowe, D. Extracting multisource brain activity from a single electromagnetic channel. Artificial Intelligence in Medicine 2003;28:89–104.CrossRefGoogle ScholarPubMed
Carmeli, C, Knyazeva, MG, Innocenti, GM, Feo, O. Assessment of EEG synchronization based on state-space analysis. Neuroimage 2005;25:339–354.CrossRefGoogle ScholarPubMed
Morgera, SS. Information theoretic complexity and its relation to pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics 1985;15:608–619.CrossRefGoogle Scholar
Inouye, T, Shinosaki, K, Sakamoto, Het al. Quantification of EEG irregularity by use of the entropy of the power spectrum. Electroencephalography and Clinical Neurophysiology 1991;79:204–210.CrossRefGoogle ScholarPubMed
Rosso, OA, Blanco, S, Yordanova, Jet al. Wavelet entropy: a new tool for analysis of short duration brain electrical signals. Journal of Neuroscience Methods 2001;105:65–75.CrossRefGoogle ScholarPubMed
Powell, CE, Percival, IC. A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems. Journal of Physics A 1979;12:2053–2071.CrossRefGoogle Scholar
Wackermann, J. Towards a quantitative characterisation of functional states of the brain: from the non-linear methodology to the global linear description. International Journal of Psychophysiology 1999;34:65–80.CrossRefGoogle ScholarPubMed
Wackermann, J. State space representation and global descriptors of the brain's electrical activity. In Training Course Textbook. Awaji Island: International Pharmaco-EEG Society; 2006, pp. 39–48.Google Scholar
Szelenberger, W, Wackermann, J, Skalski, M, Niemcewicz, S, Drojewski, J.Analysis of complexity of EEG during sleep. Acta Neurobiologiae Experimentalis 1996;56:165–169.Google ScholarPubMed
Wackermann, J. Rationality, universality, and individuality in a functional conception of theory. International Journal of Psychophysiology 2006;62:411–426.CrossRefGoogle Scholar
Szelenberger, W, Wackermann, J, Skalski, M, Drojewski, J, Niemcewicz, S. Interhemispheric differences of sleep EEG complexity. Acta Neurobiologiae Experimentalis 1996;56:955–959.Google ScholarPubMed
Saito, N, Kuginuki, T, Yagyu, Tet al. Global, regional and local measures of complexity of multichannel EEG in acute, neuroleptic-naive, first-break schizophrenics. Biological Psychiatry 1998;43:794–802.CrossRefGoogle ScholarPubMed
Pizzagalli, D, Lehmann, D, Gianotti, Let al. Brain electric correlates of strong belief in paranormal phenomena: intracerebral EEG source and regional Omega complexity analyses. Psychiatric Research and Neuroimaging 2000;100:139–154.CrossRefGoogle ScholarPubMed
Kondákor, I, Tóth, M, Wackermann, Jet al. Distribution of spatial complexity of EEG changed in idiopathic generalised epilepsy and restored by chronic valproate therapy. Brain Topography 2005;18:115–123.CrossRefGoogle Scholar
Wackermann, J.Unfolding the global complexity: topographies of complexity differentials of multi-channel EEG. In NOLTA2002, Symposium on Non-Linear Theory and Its Applications. Xi'an; October 2002, pp. 319–322.Google Scholar
Molnár, M, Csuhaj, R, Horváth, Set al. Spectral and complexity features of the EEG changed by visual input in a case of subcortical stroke compared to healthy controls. Clinical Neurophysiology 2006;117:771–780.CrossRefGoogle Scholar
Wackermann, J, Pütz, P, Gäßler, M. Unfolding EEG spatial complexity as a function of frequency. Brain Topography 2003;16:124.Google Scholar
Wackermann, J.Global characterisation of brain electrical activity by means of the Ω complexity production rate. Brain Topography 2005;18:135.Google Scholar
Pei, X, Zheng, C, Zhang, A, Duan, F, Bin, G. Discussion on “Towards a quantitative characterisation of functional states of the brain: from the non-linear methodology to the global linear description” by J. Wackermann. International Journal of Psychophysiology 2005;56:201–207.CrossRefGoogle Scholar
Allefeld, C, Wackermann, J. Omega complexity: effects of different normalization strategies. Brain Topography 2007;20:51–52.Google Scholar
Carskadon, MA, Dement, WC. Effects of total sleep loss on sleep tendency. Perception and Motor Skills 1979;48:495–506.CrossRefGoogle ScholarPubMed
Tóth, E, Kondákor, I, Túry, Fet al. Nonlinear and linear EEG complexity changes caused by gustatory stimuli in anorexia nervosa. International Journal of Psychophysiology 2004;51:253–260.CrossRefGoogle ScholarPubMed
Yoshimura, M, Isotani, T, Yagyu, Tet al. Global approach to multi-channel EEG analysis for diagnosis and clinical evaluation in mild Alzheimer's disease. Neuropsychobiology 2004;49:163–166.CrossRefGoogle Scholar
Czigler, B, Csikós, D, Hidasi, Zet al. Quantitative EEG in early Alzheimer's disease patients – power spectrum and complexity features. International Journal of Psychophysiology 2008;68:75–80.CrossRefGoogle ScholarPubMed
Irisawa, S, Isotani, T, Yagyu, Tet al. Increased Omega complexity and decreased microstate duration in nonmedicated schizophrenic patients. Neuropsychobiology 2006;54:134–139.CrossRefGoogle ScholarPubMed
Yagyu, T, Wackermann, J, Kinoshita, Tet al. Effects of chewing gum flavor onto global complexity of EEG activity. Neuropsychobiology 1997;35:46–50.CrossRefGoogle Scholar
Kondákor, I, Michel, CM, Wackermann, Jet al. Single-dose piracetam effects on global complexity measures of human spontaneous multichannel EEG. International Journal of Psychophysiology 1999;34:81–87.CrossRefGoogle ScholarPubMed
Waltinger, T, Lehmann, D, Faber, PLet al. Global dimensionality of multichannel EEG in schizophrenic patients is reduced by neuroleptic medication. Neuropsychobiology 2007;55:62.Google Scholar
Wackermann, J. From microstates to macrostates: assessment of electrical dynamics of the brain by global descriptors. In 8th World Congress of ISBET. Zurich; March 1997, p. 5.Google Scholar
Stam, CJ, Hessels-van der Leij, EM, Meulstee, J, Vliegen, JH. Changes in functional coupling between neural networks in the brain during maturation revealed by omega complexity. Clinical Electroencephalography 2000;31:104–108.CrossRefGoogle ScholarPubMed
Kim, HR, Jung, KY, Kim, SYet al. Delivery modes and neonatal EEG: spatial pattern analysis. Early Human Development 2003;75:35–53.CrossRefGoogle ScholarPubMed
Kondákor, I, Brandeis, D, Wackermann, Jet al. Multichannel EEG fields during and without visual input: Frequency domain model source locations and dimensional complexities. Neuroscience Letters 1997;226:49–52.CrossRefGoogle ScholarPubMed
Stančák, A, Wackermann, J. Spatial EEG synchronisation over sensorimotor areas in brisk and slow self-paced index finger movements. Brain Topography 1998;11:23–33.CrossRefGoogle ScholarPubMed
Stančák, A, Lücking, CH, Kristeva-Feige, R. The size of corpus callosum and functional connectivities of cortical regions in finger and shoulder movements. Cognitive Brain Research 2002;13:61–74.CrossRefGoogle ScholarPubMed
Müller, TJ, Koenig, T, Wackermann, Jet al. Subsecond changes of global brain state in illusory multistable motion perception. Journal of Neural Transmission 2005;112:565–576.CrossRefGoogle Scholar
Bhattacharya, J.Complexity analysis of spontaneous EEG. Acta Neurobiologiae Experimentalis 2000;60:495–501.Google ScholarPubMed
Bhattacharya, J, Petsche, H, Pereda, E. Long-range synchrony in the γ band: role in music perception. Journal of Neuroscience 2001;21:6329–6337.CrossRefGoogle ScholarPubMed
Isotani, T, Kinoshita, T, Lehmann, D, Pascual-Marqui, RD, Wackermann, J. Spatial configuration of brain electrical activity during positive, neutral and negative emotions. Methods and Findings in Experimental and Clinical Pharmacology 2002;24D:109–110.Google Scholar
Lehmann, D, Ozaki, H, Pal, I. EEG alpha map series: brain micro-states by space-oriented adaptive segmentation. Electroencephalography and Clinical Neurophysiology 1987;67:271–288.CrossRefGoogle ScholarPubMed
Wackermann, J. Continuity and discontinuity in models of brain electrical dynamics. Brain Topography 2006;18:223.Google Scholar
Pikovsky, A, Rosenblum, M, Kurths, J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge: Cambridge University Press; 2001.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×