Philosophical Transactions of the Royal Society B: Biological Sciences

    The power of today's laboratory equipment allows more and more data channels to be easily recorded. However, some misunderstandings about processing such multivariate data may still be found in the literature. The typical mistake is to treat a multichannel system as comprising pairs of channels; this approach does not use all the collected information about the investigated system, and may lead to erroneous conclusions. In this paper, the differences between single- and multichannel approaches will be briefly summarized and some examples of problems will be described.

    References

    • Achermann P, Hartmann R, Gunzinger A, Guggenbühl W& Borbély A.A. 1994All night sleep and artificial stochastic control have similar correlation dimension. Electroencephalogr. Clin. Neurophys. 90, 384–387. Crossref, PubMedGoogle Scholar
    • Akaike H. 1968On the use of a linear model for the identification of feedback systems. Ann. Inst. Stat. Math. 20, 425–440. Crossref, ISIGoogle Scholar
    • Blinowska K.J& Malinowski M. 1991Non-linear and linear forecasting of the EEG time series. Biol. Cybern. 66, 159–165. Crossref, PubMed, ISIGoogle Scholar
    • Blinowska K.J, Kuś R& Kamiński M. 2004Granger causality and information flow in multivariate processes. Phys. Rev. E. 70, 050902(R). Crossref, ISIGoogle Scholar
    • Caines P.E& Chan C.W. 1975Feedback between stationary stochastic processes. IEEE Trans. Autom. Control. 20, 498–508. Crossref, ISIGoogle Scholar
    • Gersch W. 1972Causality or driving in electrophysiological signal analysis. Math. Biosci. 14, 177–196. CrossrefGoogle Scholar
    • Granger C.W.J. 1969Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 37, 424–438. Crossref, ISIGoogle Scholar
    • Granger C.W.J. 1980Testing for causality: a personal viewpoint. J. Econ. Dyn. Control. 2, 329–352. Crossref, ISIGoogle Scholar
    • Jenkins G.M& Watts D.GSpectral analysis and its applications. 1968San Francisco:Holden-Day. Google Scholar
    • Jensen F.VBayesian networks and decision graphs. 2001New York:Springer. Google Scholar
    • Kamiński M& Blinowska K.J. 1991A new method of the description of the information flow. Biol. Cybern. 65, 203–210. Crossref, PubMed, ISIGoogle Scholar
    • Kamiński M, Ding M, Truccolo W& Bressler S. 2001Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol. Cybern. 85, 145–157. Crossref, PubMed, ISIGoogle Scholar
    • Korzeniewska A, Manczak M, Kamiński M, Blinowska K.J& Kasicki S. 2003Determination of information flow direction between brain structures by a modified Directed Transfer Function method (dDTF). J. Neurosci. Meth. 125, 195–207. Crossref, PubMed, ISIGoogle Scholar
    • Kuś R, Kamiński M& Blinowska K.J. 2004Determination of EEG activity propagation: pair-wise versus multichannel estimate. IEEE Trans. Biomed. Eng. 51, 1501–1510. Crossref, PubMed, ISIGoogle Scholar
    • Marple S.LDigital spectral analysis with applications. Prentice-Hall Signal Processing Series1987New Jersey:Simon & Schuster. Google Scholar
    • Pijn J.P.M, Van Neerven L, Noest A& Lopes da Silva F.H. 1991Chaos or noise in EEG signals:vh dependence on state and brain site. Electroencephalogr. Clin. Neurophys. 79, 371–381. Crossref, PubMedGoogle Scholar
    • Pijn J.P.M, Velis D.N, van der Heyden M.J, DeGoede J, van Veelen C.W.M& Lopes da Silva F.H. 1997Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings. Brain Topogr. 9, 249–270. Crossref, PubMed, ISIGoogle Scholar
    • Saito Y& Harashima HTracking of information within multichannel EEG record—causal analysis in EEG. Recent advances in EEG and EMG data processing, Yamaguchi N& Fujisawa K. 1981Amsterdam:Elsevier. Google Scholar
    • Sameshima K& Baccalá L.A. 1999Using partial directed coherence to describe neuronal ensemble interactions. J. Neurosci. Meth. 94, 93–103. Crossref, PubMed, ISIGoogle Scholar
    • Stam C, Pijn J.P.M, Suffczynski P& Lopes da Silva F.H. 1999Dynamics of the human alpha rhythm: evidence for non-linearity?. Clin. Neurophys. 110, 1801–1813. Crossref, PubMed, ISIGoogle Scholar
    • Wiener NThe theory of prediction. Modern mathematics for engineers& Beckenbach E.F. 1956New York:McGraw-Hill. Google Scholar