Block coherence: A method for measuring the interdependence between two blocks of neurobiological time series

Biological Cybernetics

Volumn 104, Issue 3, 2011, Pages 197-207

  Nedungadi, Aatira G ^a,b   Ding, Mingzhou ^c   Rangarajan, Govindan ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b CENTRE FOR CELLULAR AND MOLECULAR BIOLOGY   (India)

^c UNIVERSITY OF FLORIDA   (United States)

Author keywords

Coherence; Granger causality; Multivariate process; Spectral density matrix

Indexed keywords

BRAIN AREAS; COHERENCE; FUNCTIONAL CONNECTIVITY; GRANGER CAUSALITY; LOCAL FIELD POTENTIALS; MULTI SENSOR; MULTIVARIATE PROCESS; REGION OF INTEREST; REGIONS OF INTEREST; RESPONSE TIME; SPECTRAL DENSITY MATRIX; VISUOMOTORS;

ELECTROPHYSIOLOGY; SPECTRAL DENSITY;

TIME SERIES;

HAPLORHINI;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BRAIN; BRAIN MAPPING; ELECTROPHYSIOLOGY; HAPLORHINI; MATHEMATICS; METHODOLOGY; NEUROBIOLOGY; PHYSIOLOGY; TIME;

ANIMALS; BRAIN; BRAIN MAPPING; ELECTROPHYSIOLOGY; HAPLORHINI; MATHEMATICS; MODELS, NEUROLOGICAL; NEUROBIOLOGY; TIME;

EID: 79955837846     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-011-0429-7     Document Type: Article

References (50)

1. Z Albo G Viana Di Prisco Y Chen G Rangarajan W Truccolo J Feng RP Vertes M Ding 2004 Is partial coherence a viable technique for identifying generators of neural oscillations Biol Cybern 90 318 326 15221392 10.1007/s00422-004-0475-5 (Pubitemid 40871346)
2. LA Baccala K Sameshima 2001 Partial directed coherence: a new concept in neural structure determination Biol Cybern 84 463 474 11417058 10.1007/PL00007990 1:STN:280:DC%2BD38%2FhtlKmtQ%3D%3D (Pubitemid 33605196)
3. C Bernasconi P Konig 1999 On the directionality of cortical interactions studied by structural analysis of electrophysiological recordings Biol Cybern 81 199 210 10473845 10.1007/s004220050556 1:STN:280:DyaK1Mvgs1egsw%3D%3D (Pubitemid 129538437)
4. H Boudjellaba J Dufour R Roy 1992 Testing causality between two vectors in multivariate autoregressive moving average models J Am Stat Assoc 87 1082 1090 10.2307/2290645
5. SL Bressler R Coppola R Nakamura 1993 Episodic multiregional cortical coherence at multiple frequencies during visual task performance Nature 366 153 156 8232553 10.1038/366153a0 1:STN:280:DyaK2c%2FltVWguw%3D%3D (Pubitemid 23351818)
6. D Brillinger A Guha 2007 Mutual information in the frequency domain J Stat Plan Inference 137 3 1076 1084 10.1016/j.jspi.2006.06.026 (Pubitemid 44660771)
7. A Brovelli MZ Ding A Ledberg YH Chen R Nakamura SL Bressler 2004 Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality Proc Natl Acad Sci USA 101 9849 9854 15210971 10.1073/pnas.0308538101 1:CAS:528:DC%2BD2cXlvVahtLc%3D (Pubitemid 38869325)
8. EN Brown RE Kass PP Mitra 2004 Multiple neural spike train data analysis: state-of-the-art and future challenges Nat Neurosci 7 456 461 15114358 10.1038/nn1228 1:CAS:528:DC%2BD2cXjsFKltrg%3D (Pubitemid 38552378)
9. YH Chen G Rangarajan JF Feng MZ Ding 2004 Analyzing multiple nonlinear time series with extended Granger causality Phys Lett A 324 26 35 10.1016/j.physleta.2004.02.032 1:CAS:528:DC%2BD2cXitlGqtL0%3D
10. Y Chen SL Bressler KH Knuth WA Truccolo M Ding 2006 Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity Chaos 16 026113 16822045 10.1063/1.2208455 (Pubitemid 44000356)
11. Y Chen SL Bressler M Ding 2006 Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data J Neurosci Methods 150 228 237 16099512 10.1016/j.jneumeth.2005.06.011 (Pubitemid 43144459)
12. M Dhamala G Rangarajan M Ding 2008 Estimating Granger causality from Fourier and wavelet transforms of time series data Phys Rev Lett 100 1-4 018701 18232831 10.1103/PhysRevLett.100.018701 (Pubitemid 351388395)
13. M Dhamala G Rangarajan M Ding 2008 Analyzing information flow in brain networks with nonparametric Granger causality NeuroImage 41 354 362 18394927 10.1016/j.neuroimage.2008.02.020
14. M Ding SL Bressler W Yang H Liang 2000 Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment Biol Cybern 83 35 45 10933236 10.1007/s004229900137 1:STN:280: DC%2BD3M%2FktVyitg%3D%3D
15. Ding M, Chen Y, Bressler SL (2006) Granger causality: basic theory and applications to neuroscience. In: Schelter B, Winterhalder M, Timmer J (eds) Handbook of time series analysis. Wiley-VCH Verlag, pp 437-460
16. Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall/CRC, London
17. S Friedland 1975 Generalised Hadamard inequality and its application Linear Multilinear Algebra 2 327 333 10.1080/03081087508817076
18. KJ Friston L Harrison W Penny 2003 Dynamic causal modeling NeuroImage 19 1273 1302 12948688 10.1016/S1053-8119(03)00202-7 1:STN:280: DC%2BD3svhtVyisg%3D%3D (Pubitemid 37025831)
19. IM Gel'fand AM Yaglom 1959 Calculation of the amount of information about a random function contained in another such function Am Math Soc Transl Series 2 12 199 246
20. J Geweke 1982 Measurement of linear dependence and feedback between multiple time series J Am Stat Assoc 77 304 324 10.2307/2287238
21. J Geweke 1984 Measures of conditional linear dependence and feedback between time series J Am Stat Assoc 79 907 915 10.2307/2288723
22. C Granger 1969 Measures of conditional linear dependence and feedback between time series Econometrica 37 424 438 10.2307/1912791
23. L Harrison WD Penny KJ Friston 2003 Multivariate autoregressive modeling of fMRI time series NeuroImage 19 1477 1491 12948704 10.1016/S1053-8119(03) 00160-5 1:STN:280:DC%2BD3svhtVyhtA%3D%3D (Pubitemid 37025846)
24. W Hesse E Moller M Arnold B Schack 2003 The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies J Neurosci Methods 124 27 44 12648763 10.1016/S0165-0270(02)00366-7 (Pubitemid 36315806)
25. Hoffman KM, Kunze R (1971) Linear algebra. Prentice Hall, Englewood Cliffs, NJ, USA
26. Horn RA, Johnson CR (1990) Matrix analysis. Cambridge University Press, London
27. N Jain H-X Qi JH Kaas 2001 Longterm chronic multichannel recordings from sensorimotor cortex and thalamus of primates Prog Brain Res 130 63 72 10.1016/S0079-6123(01)30006-7 (Pubitemid 35461163)
28. MR Jarvis PP Mitra 2001 Sampling properties of the spectrum and coherency of sequences of action potentials Neural Comput 13 717 749 11255566 10.1162/089976601300014312 1:STN:280:DC%2BD3M3os1OhtA%3D%3D (Pubitemid 33594301)
29. MJ Kaminski KJ Blinowska 1991 A new method of the description of the information flow in the brain structures by a modified directed transfer function (dDTF) Biol Cybern 65 203 210 1912013 10.1007/BF00198091 1:STN:280:DyaK38%2Fgt1CisQ%3D%3D
30. M Kaminski M Ding WA Truccolo SL Bressler 2001 Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance Biol Cybern 85 145 157 11508777 10.1007/s004220000235 1:STN:280:DC%2BD3MvmtlCjsQ%3D%3D (Pubitemid 33605209)
31. A Korzeniewska M Manczak M Kaminski KJ Blinowska S Kasicki 2003 Determination of information flow direction among brain structures by a modified directed transfer function (dDTF)method J Neurosci Methods 125 195 207 12763246 10.1016/S0165-0270(03)00052-9 (Pubitemid 36579348)
32. R Kus M Kaminski KJ Blinowska 2004 Determination of EEG activity propagation: pairwise versus multichannel estimate IEEE Trans Bio-Med Eng 51 1501 1510 10.1109/TBME.2004.827929 (Pubitemid 39100223)
33. C Ladroue S Guo K Kendrick J Feng 2009 Beyond element-wise interactions: identifying complex interactions in biological processes PLoS ONE 4 9 e6899 19774090 10.1371/journal.pone.0006899
34. H Liang SL Bressler M Ding WA Truccolo R Nakamura 2002 Synchronized activity in prefrontal cortex during anticipation of visuomotor processing Neuroreport 13 2011 2015 12438916 10.1097/00001756-200211150-00004 (Pubitemid 36005915)
35. M Lungarella O Sporns 2006 Mapping information flow in sensorimotor networks PLoS Comput Biol 2 1301 1312 10.1371/journal.pcbi.0020144 1:CAS:528:DC%2BD28XhtFGitbvI (Pubitemid 44656523)
36. Lutkepohl H (1991) Introduction to multiple timeseries analysis. Springer-Verlag, Berlin
37. Mitrinovic DS, Pecaric JE, Fink AM (1993) Classical and new inequalities in analysis. Kluwer Academic Publishers, Dordrecht
38. Morf M et al (1978) Recursive multichannel maximum entropy spectral estimation. IEEE Trans GeoSci Elec, GE-16 (2), 85-94 (Pubitemid 8631419)
39. Pascual-Marqui RD (2007) Coherence and phase synchronisation: Generalisation to pairs of multivariate time-series and removal of zero led correlations. ArXiv:0706.1776v3
40. Percival DB, Walden AT (1998) Analysis for physical applications. Cambridge University Press, London, UK
41. D Prichard J Theiler 1994 Generating surrogate data for time series with several simultaneously measured variables Phys Rev Lett 73 951-954 10057582 10.1103/PhysRevLett.73.951 (Pubitemid 24976362)
42. A Roebroeck E Formisano R Goebel 2005 Mapping directed influence over the brain using Granger causality and fMRI Neuroimage 25 230 242 15734358 10.1016/j.neuroimage.2004.11.017 (Pubitemid 40289151)
43. JR Rosenberg DM Halliday P Breeze BA Conway 1998 Identification of patterns of neuronal connectivity-partial spectra, partial coherence, and neuronal interactions J Neurosci Methods 83 57 72 9765051 10.1016/S0165-0270(98) 00061-2 1:STN:280:DyaK1cvjs1Srsg%3D%3D (Pubitemid 28444960)
44. Rozanov YA (1967) Stationary random process. Holden Day, San Francisco
45. AH Sayed T Kailath 2001 A survey of spectral factorization methods Numer Linear Algebra Appl 8 467 496 10.1002/nla.250
46. Schelter B, Dahlhaus R, Leistritz L, Hesse W, Schack B, Kurths J, Timmer J, Witte H (2008) Multivariate time series analysis. In: Dahlhaus R, Kurths J, Maass P, Timmer J (eds) Mathematical methods in time series analysis and digital image processing. Springer, New York, pp 1-40
47. A Tang D Jackson J Hobbs W Chen JL Smith H Patel A Prieto D Petrusca MI Grivich A Sher P Hottowy W Dabrowski AM Litke JM Beggs 2008 A maximum entropy model applied to spatial and temporal correlations from cortical networks in vitro J Neurosci 28 2 505 518 18184793 10.1523/JNEUROSCI.3359-07.2008 1:CAS:528:DC%2BD1cXovVGhsQ%3D%3D
48. X Wang Y Chen SL Bressler M Ding 2007 Granger causality between multiple interdependent neurobiological time series: blockwise versus pairwise methods Int J Neural Syst 17 71 78 17565503 10.1142/S0129065707000944 1:CAS:528:DC%2BD1cXitlahtbk%3D (Pubitemid 46906232)
49. JH Wu XG Liu JF Feng 2008 Detecting causality between different frequencies J Neurosci Methods 167 367 375 17928062 10.1016/j.jneumeth.2007.08. 022 (Pubitemid 350235631)
50. Y Zhang Y Chen SL Bressler M Ding 2008 Response preparation and inhibition: the role of cortical sensorimotor beta rhythm Neuroscience 156 238 246 18674598 10.1016/j.neuroscience.2008.06.061 1:CAS:528:DC%2BD1cXhtFaisLvF