Abstract
An important piece of information, which can be extracted from parameters of empirical models, is quantitative characteristics of couplings between processes under study. The problem of coupling detection is encountered in multiple fields including physics (Bezruchko et al., 2003), geophysics (Maraun and Kurths, 2005; Mokhov and Smirnov, 2006, 2008; Mosedale et al., 2006; Palus and Novotna, 2006; Verdes, 2005; Wang et al., 2004), cardiology (Rosenblum et al., 2002; Palus and Stefanovska, 2003) and neurophysiology (Arnhold et al., 1999; Brea et al., 2006; Faes et al., 2008; Friston et al., 2003; Kreuz et al., 2007; Kiemel et al., 2003; Le Van Quyen et al., 1999; Mormann et al., 2000; Osterhage et al., 2007; Pereda et al., 2005; Prusseit and Lehnertz, 2008; Smirnov et al., 2005; Romano et al., 2007; Schelter et al., 2006; Schiff et al., 1996; Sitnikova et al., 2008; Smirnov et al., 2008, Staniek and Lehnertz, 2008; Tass, 1999; Tass et al., 2003). Numerous investigations are devoted to synchronisation, which is an effect of interaction between non-linear oscillatory systems (see, e.g., Balanov et al., 2008; Boccaletti et al., 2002; Hramov and Koronovskii, 2004; Kreuz et al., 2007; Maraun and Kurths, 2005; Mormann et al., 2000; Mosekilde et al., 2002; Osipov et al., 2007; Palus and Novotna, 2006; Pikovsky et al., 2001; Prokhorov et al., 2003; Tass et al., 2003). In the last decade, more careful attention is paid to directional coupling analysis. Such characteristics might help, e.g., to localise an epileptic focus (a pathologic area) in the brain from electroencephalogram (EEG) or magnetoencephalogram (MEG) recordings: hypothetically, an increasing influence of an epileptic focus on adjacent areas leads to the seizure onset for some kinds of epilepsy.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Akaike, H.: A new look at the statistical identification model. IEEE Trans. Autom. Control. 19, 716–723 (1974)
Ancona, N., Marinazzo, D., Stramaglia, S.: Radial basis function approach to nonlinear Granger causality of time series. Phys. Rev. E. 70, 056221 (2004)
Arnhold, J., Lehnertz, K., Grassberger, P., Elger, C.E.: A robust method for detecting interdependences: application to intracranially recorded EEG. Physica D. 134, 419–430 (1999)
Balanov, A., Janson, N., Postnov, D., Sosnovtseva, O.: Synchronization: From Simple to Complex. Springer, Berlin, 2008
Barnston, A.G., Livezey, R.E.: Classification, seasonality, and persistence of low frequency atmospheric circulation patterns. Mon. Wea. Rev. 115, 1083–1126 (1987)
Benabid, A.L., Pollak, P., Gervason, C., Hoffmann, D., Gao, D.M., Hommel, M., Perret, J.E., De Rougemont, J.: Long-term suppression of tremor by chronic stimulation of the ventral intermediate thalamic nucleus. The Lancet. 337, 403–406 (1991)
Benabid, A.L., Wallace, B., Mitrofanis, J., Xia, R., Piallat, B., Chabardes, S., Berger, F. A putative generalized model of the effects and mechanism of action of high frequency electrical stimulation of the central nervous system. Acta Neurol. Belg. 105, 149–157 (2005)
Bezruchko, B.P., Ponomarenko, V.I., Prokhorov, M.D., Smirnov, D.A., Tass, P.A.: Modeling nonlinear oscillatory systems and diagnostics of coupling between them using chaotic time series analysis: applications in neurophysiology. Physics – Uspekhi. 51, 304–310 (2008)
Bezruchko, B.P., Ponomarenko, V.I., Rosenblum, M.G., Pikovsky, A.S.: Characterizing direction of coupling from experimental observations. Chaos. 13, 179–184 (2003)
Boccaletti, S., Kurths, S., Osipov, G.,, Valladares, D., Zhou, C.: The synchronization of chaotic systems. Phys. Rep. 366, 1–52 (2002)
Brea, J., Russell, D.F., Neiman, A.B.: Measuring direction in the coupling of biological A case study for electroreceptors of paddlefish. Chaos. 16, 026111 (2006)
Cimponeriu, L., Rosenblum, M., Pikovsky, A.: Estimation of delay in coupling from time series. Phys. Rev. E. 70, 046213 (2004)
CLIVAR Initial Implementation Plan. WCRP No.103. WMO/TD No.869. ICPO No.14. 313pp. http://www.clivar.dkrz.de/hp.html. (1998)
Coenen, A.M.L., van Luijtelaar, E.L.J.M.: Genetic Animal models for absence epilepsy: a review of the WAG/Rij strain of rats. Behavioral Genetics. 33, 635–655 (2003)
Conway, J. et al. Evidence of interannual variability of the carbon cycle from the NOAA/CMDL global air sampling network. J. Geophys. Res. 99, 22831–22855 (1994)
Dolan, K.T., Neiman, A.: Surrogate analysis of coherent multichannel data. Phys. Rev. E. 65, 026108 (2002)
Eichler, M.: Graphical modelling of dynamic relationships in multivariate time series. In: Winterhalder, M., Schelter, B., Timmer, J. (eds) Handbook of Time Series Analysis, pp. 335–367. Wiley-VCH, Berlin (2006)
Faes, L., Porta, A., Nollo, G.: Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategies based on k nearest neighbors. Phys. Rev. E. 78, 026201 (2008)
Feldmann, U., Bhattacharya, J.: Predictability improvement as an asymmetrical measure of interdependence in bivariate time series. Int. J. Bif. Chaos. 14, 505–514 (2004)
Friston, K.J., Harrison, L., Penny, W.: Dynamic causal modelling. NeuroImage. 19, 1273–1302 (2003)
Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 37, 424–438 (1969)
Hamming, R.W.: Digital Filters. 2nd edn. Prentice-Hall, Englewood Cliffs, NJ (1983)
Hlavackova-Schindler, K., Palus, M., Vejmelka, M., Bhattacharya, J.: Causality detection based on information-theoretic approaches in time series analysis. Phys. Rep. 441, 1–46 (2007)
Houghton, J.T., Ding, Y., Griggs, D.J., Noguer, M., et al. (eds). Climate Change 2001: The Scientific Basis. Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2001)
Hramov, A.Ye., Koronovskii, A.A.: An approach to chaotic synchronization. Chaos. 14, 603–610 (2004)
Inoue, M., Duysens, J., Vossen, J.M., Coenen, A.M.: Thalamic multiple-unit activity underlying spike-wave discharges in anesthetized rats. Brain Res. 612, 35–40 (1993)
Jevrejeva, S., Moore, J., Grinsted, A. Influence of the Arctic Oscillation and El Nino – Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: The wavelet approach. J. Geophys. Res. 108(D21), 4677, doi:10.1029/2003JD003417 (2003)
Jones, E.G.: The Thalamus. Plenium Press, New York (1985)
Kiemel, T., Gormley, K.M., Guan, L., Williams, T.L., Cohen, A.H.: Estimating the strength and direction of functional coupling in the lamprey spinal cord. J. Comput. Neurosci. 15, 233–245 (2003)
Kreuz, T., Mormann, F., Andrzejak, R.G., Kraskov, A., Lehnertz, K., Grassberger, P.: Measuring synchronization in coupled model systems: A comparison of different approaches. Physica D. 225, 29–42 (2007)
Kreuz, T., Mormann, F., Andrzejak, R.G., Kraskov, A., Lehnertz, K., Grassberger, P.: Measuring synchronization in coupled model systems: A comparison of different approaches. Phys. D. 225, 29–42 (2007)
Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer, Berlin (1984)
Latif, M.: Tropical Pacific/Atlantic Ocean interactions at multidecadal time scales. Geophys. Res. Lett. 28, 539–542 (2001)
Lean, J., Rottman, G., Harder, J., Kopp, G.: Source contributions to new understanding of global change and solar variability. Solar Phys. 230, 27–53 (2005)
Le Van Quyen, M., Martinerie, J., Adam, C., Varela F.: Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy. Physica D. 127, 250–266 (1999)
Maraun, D., Kurths, J.: Epochs of phase coherence between El Nino/Southern Oscillation and Indian monsoon. Geophys. Res. Lett. 32, L15709 (2005)
Meeren, H., van Luijtelaar, G., Lopes da Silva, F., Coenen, A.: Evolving concepts on the pathophysiology of absence seizures: the cortical focus theory. Arch. Neurol. 62, 371–376 (2005)
Meeren, H.K., Pijn, J.P., van Luijtelaar, E.L., Coenen, A.M., Lopes da Silva, F.H.: Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. J. Neurosci. 22, 1480–1495 (2002)
Midzianovskaia, I.S., Kuznetsova, G.D., Coenen, A.M., Spiridonov, A.M., van Luijtelaar, E.L.: Electrophysiological and pharmacological characteristics of two types of spike-wave discharges in WAG/Rij rats. Brain Res. 911, 62–70 (2001)
Mokhov, I.I., Bezerkhny, V.A., Eliseev, A.V., Karpenko, A.A.: Interrelation between variations in the global surface air temperature and solar activity based on observations and reconstructions. Doklady Earth Sci. 409, 805–809 (2006)
Mokhov, I.I., Khvorostyanov, D.V., Eliseev, A.V.: Decadal and longer term changes in El Nino – Southern Oscillation characteristics. Intern. J. Climatol. 24, 401–414 (2004)
Mokhov, I.I., Smirnov, D.A.: Diagnostics of a cause – effect relation between solar activity and the earth’s global surface temperature. Izvestiya, atmos. Oceanic Phys. 44, 263–272 (2008)
Mokhov, I.I., Smirnov, D.A.: El Nino Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices. Geophys. Res. Lett. 33, L0378 (2006)
Mokhov, I.I., Smirnov, D.A.: Empirical estimates of the influence of natural and anthropogenic factors on the global surface temperature. Doklady Acad. Sci. 426(5), 679–684, (in Russian) (2009)
Moore, J., Grinsted, A., Jevrejeva, S.: Is there evidence for sunspot forcing of climate at multi-year and decadal periods?. Geophys. Res. Lett. 33, L17705 (2006)
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. Phys. D. 144, 358–369 (2000)
Mosedale, T.J., Stephenson, D.B., Collins, M., Mills, T.C.: Granger causality of coupled climate processes: ocean feedback on the North Atlantic Oscillation. J. Climate. 19, 1182–1194 (2006)
Mosekilde, E., Maistrenko Yu., Postnov, D.: Chaotic Synchronization. Applications to Living Systems. World Scientific, Singapore (2002)
Nini, A., Feingold, A., Slovin, H., Bergman, H.: Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. J. Neurophysiol. 74, 1800–1805 (1995)
Osipov, G.V., Kurths, J., Zhou, C.: Synchronization in Oscillatory Networks. Springer, Berlin (2007)
Osterhage, H., Mormann, F., Wagner, T., Lehnertz, K.: Measuring the directionality of coupling: phase versus state space dynamics and application to EEG time series. Int. J. Neural Syst. 17, 139–148 (2007)
Palus, M., Novotna, D.: Quasi-biennial oscillations extracted from the monthly NAO index and temperature records are phase-synchronized. Nonlin. Processes Geophys. 13, 287–296 (2006)
Palus, M., Stefanovska, A.: Direction of coupling from phases of interacting oscillators: An information-theoretic approach. Phys. Rev. E. 67, 055201(R) (2003)
Panayiotopoulos, C.P.: Absence epilepsies. In: Engel, J.J., Pedley, T.A. (eds.). Epilepsy: A Comprehensive Textbook, pp. 2327–2346. Lippincott-Raven Publishers, Philadelphia. (1997)
Pereda, E., Quian Quiroga, R., Bhattacharya, J.: Nonlinear multivariate analysis of neurophysiological signals. Progr. Neurobiol. 77, 1–37 (2005)
Pikovsky, A.S., Rosenblum, M.G., Kurths, J.: Synchronisation. A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)
Polack, P.O., Guillemain, I., Hu, E., Deransart, C., Depaulis, A., Charpier, S.: Deep layer somatosensory cortical neurons initiate spike-and-wave discharges in a genetic model of absence seizures. J. Neurosci. 27, 6590–6599 (2007)
Pozo-Vazquez, D., Esteban-Parra, M.J., Rodrigo, F.S., Castro-Diez, Y.: The association between ENSO and winter atmospheric circulation and temperature in the North Atlantic region. J. Climate. 14, 3408–3420 (2001)
Prokhorov, M.D., Ponomarenko, V.I., Gridnev, V.I., Bodrov, M.B., Bespyatov, A.B.: Synchronization between main rhythmic processes in the human cardiovascular system. Phys. Rev. E. 68, 041913 (2003)
Prusseit, J., Lehnertz, K.: Measuring interdependences in dissipative dynamical systems with estimated Fokker-Planck coefficients. Phys. Rev. E. 77, 041914 (2008)
Rivlin-Etzion, M., Marmor, O., Heimer, G., Raz, A., Nini, A., Bergman, H.: Basal ganglia oscillations and pathophysiology of movement disorders. Curr. Opin. Neurobiol. 16, 629–637 (2006)
Rogers, J.C.: The association between the North Atlantic Oscillation and the Southern Oscillation in the North Hemisphere. Mon. Wea. Rev. 112, 1999–2015 (1984)
Romano, M.C., Thiel, M., Kurths, J., Grebogi, C.: Estimation of the direction of the coupling by conditional probabilities of recurrence. Phys. Rev. E. 76, 036211 (2007)
Rosenblum, M.G., Cimponeriu, L., Bezerianos, A., et al. Identification of coupling direction: Application to cardiorespiratory interaction. Phys. Rev. E. 65, 041909 (2002)
Rosenblum, M.G., Pikovsky, A.S., Kurths, J., Schaefer, C., Tass, P.A.: Phase synchronization: from theory to data analysis. In: Moss, F., Gielen, S. (eds.) Neuro-Informatics. Handbook of Biological Physics, vol. 4, pp. 279–321. Elsevier Science, New York (2001)
Rosenblum, M.G., Pikovsky, A.S.: Detecting direction of coupling in interacting oscillator. Phys. Rev. E. 64, 045202(R) (2001)
Sato, M., Hansen, J.E., McCormick, M.P., Pollack, J.B.: Stratospheric aerosol optical depths, 1850–1990. J. Geophys. Res. 98, 22987–22994 (1993)
Schelter, B., Winterhalder, M., Eichler, M., Peifer, M., Hellwig, B., Guschlbauer, B., Luecking, C.H., Dahlhaus, R., Timmer, J.: Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Methods. 152, 210–219 (2006)
Schiff, S.J., So, P., Chang, T., Burke, R.E., Sauer, T.: Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys. Rev. E. 54, 6708–6724 (1996)
Schreiber, T., Schmitz, A.: Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77, 635–638 (1996)
Schwarz, G.: Estimating the order of a model. Ann. Stat. 6, 461–464 (1978)
Seidenbecher, T., Staak, R., Pape, H.C.: Relations between cortical and thalamic cellular activities during absence seizures in rats. Eur. J. Neurosci. 10, 1103–1112 (1998)
Sitnikova E and van Luijtelaar, G.: Cortical and thalamic coherence during spike-wave seizures in WAG/Rij rats. Epilepsy Res. 71, 159–180 (2006)
Sitnikova, E., Dikanev, T., Smirnov, D., Bezruchko, B., van Luijtelaar, G.: Granger causality: Cortico-thalamic interdependencies during absence seizures in WAG/Rij rats. J. Neurosci. Meth. 170, 245–254 (2008)
Smirnov, D., Barnikol, U.B., Barnikol, T.T., Bezruchko, B.P., Hauptmann, C., Buehrle, C., Maarouf, M., Sturm, V., Freund, H.-J., Tass, P.A.: The generation of Parkinsonian tremor as revealed by directional coupling analysis. Europhys. Lett. 83, 20003 (2008)
Smirnov, D., Schelter, B., Winterhalder, M., Timmer, J.: Revealing direction of coupling between neuronal oscillators from time series: Phase dynamics modeling versus partial directed coherence. Chaos. 17, 013111 (2007)
Smirnov, D.A., Andrzejak, R.G.: Detection of weak directional coupling: phase dynamics approach versus state space approach. Phys. Rev. E. 71, 036207 (2005)
Smirnov, D.A., Bezruchko, B.P.: Estimation of interaction strength and direction from short and noisy time series. Phys. Rev. E. 68, 046209 (2003)
Smirnov, D.A., Bodrov, M.B., Perez Velazquez, J.L., Wennberg, R.A., Bezruchko, B.P.: Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data. Chaos. 15, 024102 (2005)
Staniek, M., Lehnertz, K.: Symbolic transfer entropy. Phys. Rev. Lett. 100, 158101 (2008)
Steriade, M.: Sleep, epilepsy and thalamic reticular inhibitory neurons. Trends Neurosci. 28, 317–324 (2005)
Tass, P.A. A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biol. Cybern. 89, 81–88 (2003)
Tass, P.A., Fieseler, T., Dammers, J., Dolan, K., Morosan, P., Majtanik, M., Boers, F., Muren, A., Zilles, K., Fink, G.R. Synchronization tomography: a method for three-dimensional localization of phase synchronized neuronal populations in the human brain using magnetoencephalography. Phys. Rev. Lett. 90, 088101 (2003)
Tass, P.A., Majtanik, M.: Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study. Biol. Cybern. 94, 58–66 (2006)
Tass, P.A.: Phase Resetting in Medicine and Biology. Springer, Berlin (1999)
van Luijtelaar, E.L.J.M., Coenen, A.M.L.: Two types of electrocortical paroxysms in an inbred strain of rats. Neurosci. Lett. 70, 393–397 (1986)
Verdes, P.F.: Assessing causality from multivariate time series. Phys. Rev. E. 72, 026222 (2005)
Vergnes, M., Marescaux, C., Depaulis, A., Micheletti, G., Warter, J.M.: Spontaneous spike and wave discharges in thalamus and cortex in a rat model of genetic petit mal-like seizures. Exp. Neurol. 96, 127–136 (1987)
Wallace, J.M., Gutzler, D.S.: Teleconnections in the geopotential height field during the northern hemisphere winter. Mon. Wea. Rev. 109, 784–812 (1981)
Wang, S., Chen, Y., Ding, M., Feng, J., Stein, J.F., Aziz, T.Z., Liu, X.J.: Revealing the dynamic causal interdependence between neural and muscular signals in Parkinsonian tremor. J. Franklin Inst. 344, 180–195 (2007)
Wang, W., Anderson, B.T., Kaufmann, R.K., Myneni, R.B. The relation between the North Atlantic Oscillation and SSTs in North Atlantic basin. J. Climate. 17, 4752–4759 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bezruchko, B.P., Smirnov, D.A. (2010). Identification of Directional Couplings. In: Extracting Knowledge From Time Series. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12601-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-12601-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12600-0
Online ISBN: 978-3-642-12601-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)