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PLOS ONE  2012 

Time-Delayed Mutual Information of the Phase as a Measure of Functional Connectivity

DOI: 10.1371/journal.pone.0044633

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Abstract:

We propose a time-delayed mutual information of the phase for detecting nonlinear synchronization in electrophysiological data such as MEG. Palus already introduced the mutual information as a measure of synchronization [1]. To obtain estimates on small data-sets as reliably as possible, we adopt the numerical implementation as proposed by Kraskov and colleagues [2]. An embedding with a parametric time-delay allows a reconstruction of arbitrary nonstationary connective structures – so-called connectivity patterns – in a wide class of systems such as coupled oscillatory or even purely stochastic driven processes [3]. By using this method we do not need to make any assumptions about coupling directions, delay times, temporal dynamics, nonlinearities or underlying mechanisms. For verifying and refining the methods we generate synthetic data-sets by a mutual amplitude coupled network of R?ssler oscillators with an a-priori known connective structure. This network is modified in such a way, that the power-spectrum forms a power law, which is also observed in electrophysiological recordings. The functional connectivity measure is tested on robustness to additive uncorrelated noise and in discrimination of linear mixed input data. For the latter issue a suitable de-correlation technique is applied. Furthermore, the compatibility to inverse methods for a source reconstruction in MEG such as beamforming techniques is controlled by dedicated dipole simulations. Finally, the method is applied on an experimental MEG recording.

References

[1]  Palus M (1997) Detecting phase synchronization in noisy systems. Physics Letters A 235: 341–351.
[2]  Kraskov A, Stogbauer H, Grassberger P (2004) Estimating mutual information. Phys Rev E Stat Nonlin Soft Matter Phys 69: 066138 1–16.
[3]  Wilmer A, de Lussanet M, Lappe M (2010) A method for the estimation of functional brain connectivity from time-series data. Cognitive Neurodynamics 4: 133–149.
[4]  Pfurtscheller G, da Silva FHL (1999) Event-related EEG/MEG synchronization and desynchronization: basic principles. Clin Neurophysiol 110: 1842–1857.
[5]  Rodriguez E, George N, Lachaux JP, Martinerie J, Renault B, et al. (1999) Perception's shadow: long-distance synchronization of human brain activity. Nature 397: 430–433.
[6]  Singer W (1999) Striving for coherence. Nature 397: 391–393.
[7]  Friston KJ (2000) The labile brain. i. neuronal transients and nonlinear coupling. Phil Trans R Soc Lond B 355: 215–236.
[8]  Fries P (2005) A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in Cognitive Sciences 9: 474–480.
[9]  Fell J, Axmacher N (2011) The role of phase synchronization in memory processes. Nat Rev Neurosci 12: 105–118.
[10]  Toga AW, Mazziotta JC (2002) Brain mapping: the methods. New York: Academic Press, 2 edition.
[11]  Pine J, Taketani M, Baudry M (2006) A History of MEA Development, Springer US. pp. 3–23.
[12]  Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HD (1995) Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 51: 980–994.
[13]  Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76: 1804–1807.
[14]  Pikovsky A, Kurths J, Rosenblum M (2003) Synchronization: A universal concept in nonlinear sciences. Cambridge University Press, 1 edition.
[15]  Le Van Quyen M, Bragin A (2007) Analysis of dynamic brain oscillations: methodological advances. Trends in Neurosciences 30: 365–373.
[16]  Sakkalis V (2011) Review of advanced techniques for the estimation of brain connectivity measured with eeg/meg. Computers in Biology and Medicine 41: 1110–1117.
[17]  Schack B, Grieszbach G, Krause W (1999) The sensitivity of instantaneous coherence for considering elementary comparison processing. part i: the relationship between mental activities and instantaneous EEG coherence. International Journal of Psychophysiology 31: 219–240.
[18]  Canolty RT, Knight RT (2010) The functional role of cross-frequency coupling. Trends in Cognitive Sciences 14: 506–515.
[19]  Lachaux JP, Rodriguez E, Martinerie J, Varela FJ (1999) Measuring phase synchrony in brain signals. Hum Brain Mapp 8: 194–208.
[20]  Rosenblum MG, Pikovsky AS, Kurths J (1997) From phase to lag synchronization in coupled chaotic oscillators. Phys Rev Lett 78: 4193–4196.
[21]  Stam CJ, Nolte G, Daffertshofer A (2007) Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources. Hum Brain Mapp 28: 1178–1193.
[22]  Varela FJ, Lachaux JP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2: 229–239.
[23]  Tass P, Rosenblum MG, Weule J, Kurths J, Pikovsky A, et al. (1998) Detection of n:m phase locking from noisy data: application to magnetoencephalography. Phys Rev Lett 81: 3291–3294.
[24]  Atmanspacher H, Rotter S (2008) Interpreting neurodynamics: concepts and facts. Cognitive Neurodynamics 2: 297–318.
[25]  Le Van Quyen M, Chavez M, Rudrauf D, Martinerie J (2003) Exploring the nonlinear dynamics of the brain. Journal of Physiology-Paris 97: 629–639.
[26]  Stam CJ, Breakspear M, van Cappellen van Walsum AM, van Dijk BW (2003) Nonlinear synchronization in eeg and whole-head meg recordings of healthy subjects. Human Brain Mapping 19: 63–78.
[27]  Uhlhaas PJ, Pipa G, Lima B, Melloni L, Neuenschwander S, et al. (2009) Neural synchrony in cortical networks: history, concept and current status. Frontiers in integrative neuroscience 3.
[28]  Vicente R, Wibral M, Lindner M, Pipa G (2011) Transfer entropy—a model-free measure of effective connectivity for the neurosciences. Journal of Computational Neuroscience 30: 45–67.
[29]  Uhlhaas PJ, Roux F, Rodriguez E, Rotarska-Jagiela A, Singer W (2010) Neural synchrony and the development of cortical networks. Trends in Cognitive Sciences 14: 72–80.
[30]  Gross J, Kujala J, H?m?l?inen M, Timmermann L, Schniltzler A, et al. (2001) Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc Nat Acad Sci USA 98: 694–699.
[31]  Hadjipapas A, Hillebrand A, Holliday IE, Singh KD, Barnes GR (2005) Assessing interactions of linear and nonlinear neuronal sources using MEG beamformers: a proof of concept. Clinical Neurophysiology 116: 1300–1313.
[32]  Steinberg C, Dobel C, Schupp HT, Kissler J, Elling L, et al. (2011) Rapid and highly resolving: affective evaluation of olfactorily conditioned faces. Journal of Cognitive Neuroscience 24: 17–27.
[33]  Nolte G, Meinecke FC, Ziehe A, Müller KR (2006) Identifying interactions in mixed and noisy complex systems. Physical Review E 73: 051913.
[34]  Quian Quiroga R, Kraskov A, Kreuz T, Grassberger P (2002) Performance of different synchronization measures in real data: a case study on electroencephalographic signals. Physical Review E 65.
[35]  Le Van Quyen M, Martinerie J, Adam C, Varela FJ (1999) Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy. Physica D: Nonlinear Phenomena 127: 250–266.
[36]  Le Van Quyen M, Adam C, Baulac M, Martinerie J, Varela FJ (1998) Nonlinear interdependencies of EEG signals in human intracranially recorded temporal lobe seizures. Brain Research 792: 24–40.
[37]  Gilden DL, Thornton T, Mallon MW (1995) 1/f noise in human cognition. Science 267: 1837–1839.
[38]  Linkenkaer-Hansen K, Nikouline VV, Palva JM, Ilmoniemi RJ (2001) Long-range temporal correlations and scaling behavior in human brain oscillations. The Journal of Neuroscience 21: 1370–1377.
[39]  H?m?l?inen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV (1993) Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain. Reviews of Modern Physics 65: 413–497.
[40]  Hyv?rinen A (2001) Independent component analysis. Neural Computing Surveys 2.
[41]  Genovese CR, Lazar NA, Nichols T (2002) Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage 15: 870–878.
[42]  Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B (Methodological) 57: 289–300.
[43]  Oostenveld R, Fries P, Maris E, Schoffelen JM (2011) FieldTrip: open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data. Computational Intelligence and Neuroscience 2011.
[44]  Van Veen BD, van Drongelen W, Yuchtman M, Suzuki A (1997) Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed 44: 867–880.
[45]  Le Van Quyen M, Foucher J, Lachaux J, Rodriguez E, Lutz A, et al. (2001) Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. J Neurosci Methods 111: 83–98.
[46]  Rosenblum M, Pikovsky A, Kurths J, Sch?fer C, Tass PA (2001) Phase synchronization: from theory to data analysis. In: Moss F, Gielen S, editors, Handbook of Biological Physics, Elsevier Science, volume 4: Neuro-informatics, chapter 9. pp. 279–321.
[47]  Friston KJ (1994) Functional and effective connectivity in neuroimaging: a synthesis. Human Brain Mapping 2: 56–78.
[48]  Cover TM, Thomas JA (1991) Elements of information theory. New York: John Wiley and Sons, Inc., 2 edition.
[49]  Victor JD (2002) Binless strategies for estimation of information from neural data. Physical Review E 66: 051903–1–15.
[50]  Hlavácková-Schindler K, Palus M, Vejmelka M, Bhattacharya J (2007) Causality detection based on information-theoretic approaches in time series analysis. Physics Reports 441: 1–46.
[51]  Nolte G, Bai O, Wheaton L, Mari Z, Vorbac S, et al. (2004) Identifying true brain interaction from EEG data using the imaginary part of coherency. Clinical Neurophysiology 115: 2292–2307.
[52]  Jansen B, Rit V (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics 73: 357–366.
[53]  David O, Harrison L, Friston KJ (2005) Modelling event-related responses in the brain. NeuroImage 25: 756–770.
[54]  Kiebel SJ, David O, Friston KJ (2006) Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization. NeuroImage 30: 1273–1284.
[55]  R?ssler OE (1976) An equation for continuous chaos. Physics Letters A 57: 397–398.
[56]  Roelfsema PR, Engel AK, K?nig P, Singer W (1997) Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385: 157–161.
[57]  Tallon-Baudry C, Bertrand O, Fischer C (2001) Oscillatory synchrony between human extrastriate areas during visual short-term memory maintenance. Journal of Neuroscience 21: 1–5.
[58]  Hinrichs H, Noesselt T, Heinze HJ (2008) Directed information flow—a model free measure to analyze causal interactions in event related EEG-MEG-experiments. Human Brain Mapping 29: 193–206.
[59]  Brookes MJ, Vrba J, Robinson SE, Stevenson CM, Peters AM, et al. (2008) Optimising experimental design for MEG beamformer imaging. NeuroImage 39: 1788–1802.
[60]  Fuchs M, Wagner M, Wischmann HA, K?hler T, Thei?en A, et al. (1998) Improving source reconstructions by combining bioelectric and biomagnetic data. Electroencephalography and Clinical Neurophysiology 107: 93–111.
[61]  Hillebrand A, Barnes GR (2002) A quantitative assessment of the sensitivity of whole-head MEG to activity in the adult human cortex. NeuroImage 16: 638–650.
[62]  Sekihara K, Nagarajan SS, Poeppel D, Marantz A (2002) Performance of an MEG adaptivebeamformer technique in the presence of correlated neural activities: effects on signal intensity and time-course estimates. IEEE Transactions on Biomedical Engineering 49: 1534–1546.
[63]  Barnes GR, Hillebrand A (2003) Statistical attering of MEG beamformer images. Hum Brain Mapp 18: 1–12.
[64]  Hillebrand A, Singh KD, Holliday IE, Furlong PL, Barnes GR (2005) A new approach to neuroimaging with magnetoencephalography. Hum Brain Mapp 25: 199–211.
[65]  de Munck JC, Vijn PCM, Lopes da Silva FH (1992) A random dipole model for spontaneous brain activity. IEEE Transactions on Biomedical Engineering 39: 791–804.
[66]  Goldenholz DM, Ahlfors SP, H?m?l?inen MS, Sharon D, Ishitobi M, et al. (2009) Mapping the signal-to-noise-ratios of cortical sources in magnetoencephalography and electroencephalography. Human Brain Mapping 30: 1077–1086.
[67]  Quraan MA, Moses SN, Hung Y, Mills T, Taylor MJ (2011) Detection and localization of hippocampal activity using beamformers with MEG: a detailed investigation using simulations and empirical data. Human Brain Mapping 32: 812–827.
[68]  Huang MX, Mosher JC, Leahy RM (1999) A sensor-weighted overlapping-sphere head model and exhaustive head model comparison for MEG. Physics in Medicine and Biology 44: 423.
[69]  Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. Neuroimage 19: 1273–1302.
[70]  Robinson SE, Vrba J (1998) Functional neuroimaging by synthetic aperture magnetometry SAM. In: Biomag 2000, 11 th International Conference on Biomagnetism. Sendai, Japan, pp. 1–4.
[71]  Barnes GR, Hillebrand A, Fawcett IP, Singh KD (2004) Realistic spatial sampling for MEG beamformer images. Hum Brain Mapp 23: 120–127.
[72]  Vrba J (2002) Magnetoencephalography: the art of finding a needle in a haystack. Physica C: Superconductivity 368: 1–9.
[73]  H?m?l?inen M, Ilmoniemi R (1994) Interpreting magnetic fields of the brain: minimum norm estimates. Medical and Biological Engineering and Computing 32: 35–42.
[74]  Schoffelen JM, Gross J (2009) Source connectivity analysis with meg and eeg. Human Brain Mapping 30: 1857–1865.
[75]  Vinck M, Oostenveld R, van Wingerden M, Battaglia F, Pennartz CMA (2011) An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. Neuro Image 55: 1548–1565.
[76]  Mormann F, Lehnertz K, David P, Elger C (2000) Mean phase coherence as a measure for phase synchronizationand its application to the EEG of epilepsy patients. Physica D 144: 358–369.
[77]  Chumbley JR, Friston KJ (2009) False discovery rate revisited: FDR and topological inference using Gaussian random fields. Neuro Image 44: 62–70.
[78]  Chumbley J, Worsley K, Flandin G, Friston K (2010) Topological FDR for neuroimaging. Neuro Image 49: 3057–3064.
[79]  Wibral M, Rahm B, Rieder M, Lindner M, Vicente R, et al. (2011) Transfer entropy in magnetoencephalographic data: Quantifying information ow in cortical and cerebellar networks. Progress in Biophysics and Molecular Biology 105: 80–97.
[80]  Wiener N (1956) The theory of prediction. Number 103-401-829 in Mathematics. Beckenbach, E.F., New York: McGraw-Hill.
[81]  Seth A (2008) Causal networks in simulated neural systems. Cognitive Neurodynamics 2: 49–64.
[82]  Blinowska KJ, Kus R, Kaminski M (2004) Granger causality and information ow in multivariate processes. Phys Rev E Stat Nonlin Soft Matter Phys 70: 050902.
[83]  Kaminski M, Blinowska K (1991) A new method of the description of the information ow in the brain structures. Biological Cybernetics 65: 203–210.
[84]  Nalatore H, Ding M, Rangarajan G (2007) Mitigating the effects of measurement noise on Granger causality. Physical Review E 75: 031123–1–10.
[85]  Nolte G, Ziehe A, Nikulin VV, Schl?gl A, Kr?mer N, et al. (2008) Robustly estimating the ow direction of information in complex physical systems. Physical Review Letters 100: 234101.
[86]  Penny WD, Stephan KE, Mechelli A, Friston KJ (2004) Comparing dynamic causal models. Neuro Image 22: 1157–1172.
[87]  Friston KJ, Dolan RJ (2010) Computational and dynamic models in neuroimaging. Neuro Image 52: 752–765.
[88]  David O, Kiebel SJ, Harrison LM, Mattout J, Kilner JM, et al. (2006) Dynamic causal modeling of evoked responses in EEG and MEG. Neuroimage 30: 1255–1272.
[89]  Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K (2008) The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput Biol 4.
[90]  Schreiber T (2000) Measuring information transfer. Physical Review Letters 85.
[91]  Gómez-Herrero G, Wu W, K R, Soriano MC, Pipa G, et al. (2010) Assessing coupling dynamics from an ensemble of time series. CoRR abs/1008.0539.
[92]  Vakorin VA, Krakovska O, McIntosh AR (2009) Confounding effects of indirect connections on causality estimation. Journal of Neuroscience Methods 184: 152–160.
[93]  Vakorin VA, Misic B, Krakovska O, McIntosh AR (2011) Empirical and theoretical aspects of generation and transfer of information in a neuromagnetic source network. Frontiers in Systems Neuroscience 5: 1–12.
[94]  Takens F, Rand D, Young LS (1981) Detecting strange attractors in turbulence, Springer Berlin/Heidelberg, volume 898. pp. 366–381.

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