Summary
The structure of the normal resting EEG crosspectrum Svv(ω) is analyzed using complex multivariate statistics. Exploratory data analysis with Principal Component Analysis (PCA) is followed by hypothesis testing and computer simulations related to possible neural generators. The Svv(ω) of 211 normal individuals (ages 5 to 97) may be decomposed into two types of processes: the ξ process with spatial isotropicity reflecting diffuse, correlated cortical generators with radial symmetry, and processes that seem to be generated by more spatially concentrated, correlated sources. The latter are reflected as spectral peaks such as the process. The eigenvectors of the ξ process are the Spherical Harmonic Functions which explains the recurring pattern of maps characteristic of the spatial PCA of qEEG data. A new method for estimating sources in the frequency domain which fits dipoles to the whole crosspectrum is applied to explain the characteristics of the localized sources.
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Alvarez, A., Pascual, R. and Valdes, P. Spatiotemporal properties of the a rhythm. In: E.R. John (Ed.), Machinery of the mind. Birkhauser, Boston-Basel-Berlin, 1990, 59–90.
Basar, E., Basar-Eroglu, C., Roschke, J. and Schult, J. Strange attractors EEG as sign of cognitive function. In: E.R. John (Ed.), Machinery of The Mind. Birkhauser, Boston-Basel-Berlin, 1990, 91–114.
Brillinger, R.D. Time Series: Data Analysis and Theory (Expanded Edition). Holt, Rinehart and Winston, Inc., New York, 1981.
Burg, J.P., Luenberger, D.G. and Wenger, D.L. Estimation of structured covariance matrices. Proc. IEEE, 1982, 70: 963–974.
Chapman, R.M., Ilmoniemi, R.J., Barbanera, S. and Romani, G.L. Selective localization of alpha brain activity with neuromagnetic measurements. Electoenceph. clin. Neurophysiol., 1984, 58: 569–572.
Duffy, F.H., Iyer, V.G., and Surwillo, W.W. Clinical Electroencephalography and Topographic Brain Mapping. Technology and Practice. Springer-Verlag, New York, 1989.
Duffy, F.H., Jones, K., Bartels, P., Albert, M., McAnulty, G.B. and Als, H. Quantitative neurophysiology with mapping: statistical inference, exploratory and confirmatory data analysis. Brain Topography, 1990, 3(1): 3–12.
Flury, B. Common Principal Components and Related Multivariate Models. John Wiley & Sons, New York, 1988.
Gersch, W. Non-stationary multichannel time series analysis. In A.S. Gevins and A Remond (Eds.), Handbook of Electroncephalography and Clinical Neurophysiology. Revised series Elsevier New York, 1987, Vol 1, 261–293.
Gonzalez, S.L., Grave de Peralta, R., Biscay, R., Jimenez, J.C., Pascual, R.D., Lemagne, J. and Valdes, P. Projective methods for the magnetic direct problem. In: S.J. Williamson, M. Hoke, G. Stroink and M. Kotani (Eds.), Advances in Biomagnetism. Plenum Press, New York and London, 1989, 615–618.
Grave de Peralta, R., Valdes, P., and Pascual, R. Source localization of the EEG spectrum. Presented at the Second International congress on Brain Electromagnetic Topography. Toronto, Canada, 1991.
Hannan, E.J. Multiple time series. John Wiley and Sons, Inc., New York, 1970.
Harner, R.N. Singular value descomposition: a general linear model for analysis of multivariate structure in the electroencephalogram. Brain Topography, 1990, 3(1): 43–47.
Hernandez, J., Valdes, P. and Pascual, R. A general scale factor for EEG Topography. Presented at the Second International Congress on Brain Electromagnetic Topography. Toronto, Canada, 1991.
Herrmann, W.M., Roehmel, J., Streitberg, B. and Willmann, J. Example for applying the COMSTAT algorithm to electroencephalogram data to describe variance sources. Neuropsychobiology, 1983, 10: 164–172.
Ilmoniemi, R.J., Williamson, S.J. and Hostetler, W.E. New method for study of spontaneous brain activity. In: K. Atsumi, M. Kotani, S. Ueno, T. Katila and S.J. Williamson (Eds.), Biomagnetism '87, Tokyo Denki University Press, 1988, 182–185.
Ingber, L. and Nunez, P.L. Multiple scales of statistical physics of the neocortex: applications to electroencephalography. Mathl Comput. Modeling, 1990, 13: 83–95.
John, E.R., Prichep, P. and Easton, P. Normative data banks and neurometrics. Basic concepts, methods and results of norm constructions. In: A.S. Gevins and A. Remond (Eds.), Handbook of Electroencephalography and Clinical Neurophysiology, vol. 1. Elsevier Science Publishers B. V., Amsterdam, New York, Oxford, 1987, 449–495.
Katznelson, R.D. Deterministic and Stochastic Field Theoretic Model in the Neurophysics of EEG. Ph.D Thesis Desertation, University of California at San Diego, 1982.
Lehmann, D. Brain electric micro-estate and cognition: the atoms of thought. In: E.R. John (Ed.), Machinery of the Mind. Birkhauser, Boston-Basel-Berlin, 1990a, 209–224.
Lehmann, D. and Michel, C.M. Intracerebral dipole source localization for FFT power maps. Electroenceph. clin. Neurophysiol., 1990, 76: 271–276.
Lopes da Silva, F.H. Dynamics of EEGs as signals of neural populations: models and theoretical considerations. In: E. Niedermeyer and F.H Lopes da Silva (Eds.), Electroencephalography: Basic principles, clinical applications and related fields, Urban & Schwarzenberg, Baltimore-Munich, 1987, 15–28.
Lopes da Silva, F.H. and Van Rotterdam, A., Barts, P., Van Heusden, E. and Burr, W. Models of neuronal population. The basis mechanisms of rhythmicity. In: D. Swaab and M.A. Corner (Eds.), Progress in Brain Research, 1976, Elsevier, Amsterdam, 281–308.
Lopes da Silva, F.H. and Spekreijse, H. Localization of brain sources of visually evoked responses: using single and multiple dipoles. An overview of different approaches, 1991 (in press).
Lumeau, B., Rondouin, G. and Clergeot, H. High resolution methods: an approach to the localization of generators relative to Evoked Potentials. Electroenceph. clin. Neurophysiol. Supplement, 1990, 75: 586–587.
Lutkenhoner, B. Frequency-domain localization of intracerebral dipole sources. Electroenceph. clin. Nuerophysiol., 1992, 82: 112–118.
Mocks, J. The influence of latency variations in principal component analysis of event related potentials. Psychophysiology, 1986, 23: 480–484.
Mosher, J.C., Lewis, P.S., Leahy, R. and Manbir, S. Multiple diplole modeling of spatio-temporal MEG data. SPIE Proceedings Series. July 1990. Volume 1351.
de Munck, J.C. Random dipoles as a model for spontaneous EEG and MEG activity. In: S.J. Williamson et al. (Eds.), Advances in Biomagnetism, Plenum Press, New York, 1989, 595–598.
Nunez, P. Electrical Fields of the Brain: the Neurophysics of EEG. Oxford Univ. Press, New York, 1981.
Nunez, P.L. Generation of human EEG by a combination of long and short range neocortical interactions. Brain Topography, 1989, 1: 199–215.
Pascual, R., Valdes, P. and Alvarez, A. Multivariate spectral modelling of the EEG: the xa model. Neuroscience Branch, Technical Report No. NC-001, Havana, National Center for Scientific Research, 1985.
Pascual, R.D., Valdes, P.A. and Alvarez, A. A parametric model for multichannel EEG spectra. Int. J. Neurosc., 1988, 40: 89–99.
Scherg, M. and von Cramon, D. Dipole source potentials of the auditory cortex in normal subjects and in patients with temporal lobe lesion. In: F. Grandori, M. Hoke and G.L. Romani (Eds.), Auditory Evoked Magnetic Fields and Electric Potentials. Karger, Basel, 1990, 165–193.
Silberstein, R.B., Cadusch, P.J. and Schier, M.A. Volume conduction effects on spatial principal components analysis of scalp recorded brain electrical activity. Brain Topography, 1990, 3(1): 273–274.
Siotani, M., Takesi, H. and Yasunori, F. Modern Multivariate Statistical Analysis: A Graduate Course and Handbook. American Sciences Press, Inc., Columbus, 1983.
Skrandies, W. Global field power and topography similarity. Brain Topography, 1990, 3(1): 137–141.
Stoica, Petre and Sharman, K.C. Maximum Likelihood Methods for Direction-of-Arrival Estimation. IEEE Transactions on Acoustics, Speech and Signal Processing. 1990 38 (7): 1132–1143.
Thatcher, R.W., Krause, P. and Hrybyk, M. Corticocortical association fibers and EEG coherence: a two compartmental model. Electroenceph. Clin. Neurophysiol., 1986, 64: 123–143.
Valdes, P.A. Statistical Bases. In: T. Harmony (Ed.), Functional Neuroscience Vol. III. Neurometric assessment of brain dysfunction in neurological patients, Lawrence Erlbaum Associates, Hillsdale, New Jersey, 1984, 141–254.
Valdes, P.A., Pascual, R.D., Jimenez, J.C., Biscay, R., Carballo, J.A. and Gonzalez, S.L. Functionally based statistical methods for the analysis of the EEG and event related potentials. In: J.L. Willems, J.H. Bemmel and J. Michel (Eds.), Progress in computer assisted function analysis, North-Holland, Amsterdam-New York-Oxford, 1988, 91–96.
Valdes, P. and Biscay, R. The statistical analysis of brain images. In: E.R. John (Ed.), Machinery of the Mind. Birkhauser, Boston-Basel-Berlin, 1990a, 405–434.
Valdes, P., Biscay, R., Galan, L., Bosch, J., Szava, S., and Virues, T. High resolution spectral EEG norms for topography. Brain Topography, 1990b, 3(1): 281–282.
Valdes, P., Riera, J., and Baez, O. The Genesis of EEG spatial principal components. Presented at the Second International Congress on Brain Electromagnetic Topography. Toronto, Canada, 1991.
Van Rotterdam, A., Lopes da Silva, F.H., van den Ende, J., Viergever, M.A. and Hermans, A.J. A model of the spatialtemporal charateristics of the alpha rhythm. Bull. Math. Biol., 1982, 44: 283–305.
Williamson, S.J., Wang, J.Z. and Ilmoniemi, R.J. Methods for locating sources of human alpha activity. In: S.J. Williamson, M. Hoke, G. Stroink and M. Kotani (Eds.), Advances in Biomagnetism. Plenum Press, New York and London, 1989, 257–260.
Zetterberg, L.H. Estimation of parameters for a linear difference equation with application to EEG analysis. Math. Biosciences, 1969, 5: 227–275.
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The authors of this paper wish to thank Drs. R. Silberstein, F. Lopes da Silva, D. Lehmann, M. Scherg and a referee for valuable observations that improved the original manuscript.
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Valdés, P., Bosch, J., Grave, R. et al. Frequency domain models of the EEG. Brain Topogr 4, 309–319 (1992). https://doi.org/10.1007/BF01135568
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DOI: https://doi.org/10.1007/BF01135568