Abstract
Over the last 20 years, a body of techniques known as high resolution EEG has allowed precise estimation of cortical activity from non-invasive EEG measurements. The availability of cortical waveforms from non-invasive EEG recordings allows to have not only the level of activation within a single region of interest (ROI) during a particular task, but also to estimate the causal relationships among activities of several cortical regions. However, interpreting resulting connectivity patterns is still an open issue, due to the difficulty to provide an objective measure of their properties across different subjects or groups. A novel approach addressed to solve this difficulty consists in manipulating these functional brain networks as graph objects for which a large body of indexes and tools are available in literature and already tested for complex networks at different levels of scale (Social, WorldWideWeb and Proteomics). In the present work, we would like to show the suitability of such approach, showing results obtained comparing separately two groups of subjects during the same motor task and two different motor tasks performed by the same group. In the first experiment two groups of subjects (healthy and spinal cord injured patients) were compared when they moved and attempted to move simultaneously their right foot and lips, respectively. The contrast between the foot–lips movement and the simple foot movement was addressed in the second experiment for the population of the healthy subjects. For both the experiments, the main question is whether the “architecture” of the functional connectivity networks obtained could show properties that are different in the two groups or in the two tasks. All the functional connectivity networks gathered in the two experiments showed ordered properties and significant differences from “random” networks having the same characteristic sizes. The proposed approach, based on the use of indexes derived from graph theory, can apply to cerebral connectivity patterns estimated not only from the EEG signals but also from different brain imaging methods.
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References
Albert R, Jeong H, Barabasi A. Error and attack tolerance of complex networks. Nature 2000;406:378–82
Albert R, Barabasi A. Statistical mechanic of complex networks. Rev Modern Phys 2002;74:47–97
Astolfi L, Cincotti F, Mattia D, Babiloni C, Carducci F, Basilisco A, et al. Assessing cortical functional connectivity by linear inverse estimation and directed transfer function: simulations and application to real data. Clin Neurophysiol 2005;116(4):920–32
Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccalà L, De Vico Fallani F, et al. A comparison of different cortical connectivity estimators for high resolution EEG recordings. Hum. Brain Mapp 2007;28(2):143–57
Babiloni F, Babiloni C, Locche L, Cincotti F, Rossini PM, Carducci F. High-resolution electroencephalogram: source estimates of Laplacian-transformed somatosensory-evoked potentials using a realistic subject head model constructed from␣magnetic resonance images. Med Biol Eng Comput 2000;38(5):512–9
Babiloni F, Cincotti F, Babiloni C, Carducci F, Basilisco A, Rossini PM, et al. Estimation of the cortical functional connectivity with the multimodal integration of high resolution EEG and fMRI data by Directed Transfer Function. Neuroimage 2005;24(1):118–31
Babiloni F, Babiloni C, Carducci F, Romani GL, Rossini PM, Angelone LM, et al. Multimodal integration of high-resolution EEG and functional magnetic resonance imaging data: a simulation study. Neuroimage 2003;19(1):1–15
Barabasi AL, Albert R. Emergence of scaling in random networks. Science 1999;286:509–12
Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. Complex networks: structure and dynamics. Phys Rep 2006; 424:175–308
Buchel C, Friston KJ. Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modeling and fMRI. Cereb Cortex 1997;7(8):768–78
Clifford Carter G. Coherence and time delay estimation. Proc IEEE 1987;75:236–55
Dale A, Liu A, Fischl B, Buckner R, Belliveau JW, Lewine J, Halgren E. Dynamic statistical parametric mapping: combining fMRI and mEG for high-resolution imaging of cortical activity. Neuron 2000;26(1): 55–67
Gevins A, Brickett P, Reutter B, Desmond J. Seeing through the skull: advanced EEGs use MRIs to accurately measure cortical activity from the scalp. Brain Topogr 1991;4:125–31
Gevins A, Le J, Leong H, McEvoy LK, Smith ME. Deblurring. J Clin Neurophysiol 1999;16(3):204–13
Gevins AS, Cutillo BA, Bressler SL, Morgan NH, White RM, Illes J, et al. Event-related covariances during a bimanual visuomotor task. II. Preparation and feedback. Electroencephalogr Clin Neurophysiol 1989;74:147–60
Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 1969;37: 424–38
Grave de Peralta Menendez R, Gonzalez Andino SL. Distributed source models: standard solutions and new developments. In: Uhl C, editor. Analysis of neurophysiological brain functioning. Springer Verlag; 1999. p. 176–201
Gross J, Kujala J, Hämäläinen M, Timmermann L, Schnitzler A, Salmelin R. Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc Natl Acad Sci USA 2001;98(2):694–9
Gross J, Timmermann L, Kujala J, Salmelin R, Schnitzler A. Properties of MEG tomographic maps obtained with spatial filtering. NeuroImage 2003;19:1329–36
Harary F. Graph theory. Reading, Mass: Addison-Wesley; 1969
He B, Zhang Z, Lian J, Sasaki H, Wu S, Towle VL. Boundary element method based cortical potential imaging of somatosensory evoked potentials using subjects’ magnetic resonance images. NeuroImage 2002;16:564–76
He B, Lian J. Spatio-temporal functional neuroimaging of brain electric activity. Crit Rev Biomed Eng 2002;30:283–306
Hilgetag CC, Burns GAPC, O’Neill MA, Scannell JW, Young MP. Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos Trans Roy Soc Lond B Biol Sci 2000;355:91–110
Kaminski M, Ding M, Truccolo WA, Bressler S. Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol Cybern 2001;85:145–57
Kaminski M, Blinowska K. A new method of the description of the information flow in the brain structures. Biol Cybern 1991;65:203–10
Kus R, Kaminski M, Blinowska KJ. Determination of EEG activity propagation: pair-wise versus multichannel estimate. IEEE Trans Biomed Eng 2004;51(9):1501–10
Latora V, Marchiori M. Efficient behavior of small-world networks. Phys Rev Lett 2001;87:198701
Latora V, Marchiori M. Economic small-world behavior in weighted networks. Eur Phys J B 2003;32:249–63
McIntosh AR, Gonzalez-Lima F. Structural equation modeling and its application to network analysis in functional brain imaging. Hum Brain Mapp 1994;2:2–22
Micheloyannis S, Pachou E, Stam CJ, Vourkas M, Erimaki S, Tsirka V. Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis. Neurosci Lett 2006;402:273–7
Nunez PL. Neocortical dynamics and human EEG rhythms. Oxford University Press; 1995
Pascual-Marqui RD. Reply to comments by Hamalainen, Ilmoniemi and Nunez. In: Skrandies W, editor. ISBET Newsletter N. 6, December 1995. p. 16–28
Raineteau O, Schwab M. Plasticity of motor systems after incomplete spinal cord injury. Nature 2001;2(4):263–73
Salvador R, et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 2005; 15(9):1332–42
Sivan E, Parnas H, Dolev D. Fault tolerance in the cardiac ganglion of the lobster. Biol Cybern 1999;81:11–23
Sporns O, Chialvo DR, Kaiser M, Hilgetag CC. Organization, development and function of complex brain networks. Trends Cogn Sci 2004;8:418–25
Sporns O, Zwi JD. The small world of the cerebral cortex. Neuroinformatics 2004;2:145–62
Stam CJ. Functional connectivity patterns of human magnetoencephalographic recordings: a ‹small-world’ network? Neurosci Lett 2004;355:25–28
Stam CJ, Jones BF, Manshanden I, van Cappellen van Walsum AM, Montez T, Verbunt JP, et al. Magnetoencephalographic evaluation of resting-state functional connectivity in Alzheimer’s disease. Neuroimage 2006a;32(3):1335–44
Stam CJ, Jones BF, Nolte G, Breakspear M, Scheltens P. Small-world networks and functional connectivity in Alzheimer’s disease. Cereb Cortex 2006b;17(1):92–9
Strogatz SH. Exploring complex networks. Nature 2001;410: 268–76
Urbano A, Babiloni C, Onorati P, Babiloni F. Dynamic functional coupling of high resolution EEG potentials related to unilateral internally triggered one-digit movements. Electroencephalogr Clin Neurophysiol 1998;106(6):477–87
Wang XF, Chen G. Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst Magazine 2003;3(1):6–20
Watts DJ, Strogatz SH. Collective dynamics of ‹small-world’ networks. Nature 1998, 393: 440–2
Acknowledgments
This study was performed with support of the Minister for Foreign Affairs, Division for the Scientific and Technologic Development, in the framework of a bilateral project between Italy and China (Tsinghua University), project and the support of the RIKEN Institute, Japan. This work is also supported by the European IST Programme FET Project FP6-003758. This paper only reflects the authors’ views and funding agencies are not liable for any use that may be made of the information contained herein.
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De Vico Fallani, F., Astolfi, L., Cincotti, F. et al. Extracting Information from Cortical Connectivity Patterns Estimated from High Resolution EEG Recordings: A Theoretical Graph Approach. Brain Topogr 19, 125–136 (2007). https://doi.org/10.1007/s10548-007-0019-0
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DOI: https://doi.org/10.1007/s10548-007-0019-0