Brain Topography

, Volume 23, Issue 4, pp 344–354 | Cite as

Multiple Pathways Analysis of Brain Functional Networks from EEG Signals: An Application to Real Data

  • Fabrizio De Vico Fallani
  • Francisco Aparecido Rodrigues
  • Luciano da Fontoura Costa
  • Laura Astolfi
  • Febo Cincotti
  • Donatella Mattia
  • Serenella Salinari
  • Fabio Babiloni
Original Paper

Abstract

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R h as the number of parallel paths and the global network permeability P h as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P h of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3–6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R h . The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

Keywords

Cortical networks Graph theory Redundancy Permeability Spinal cord injury 

Notes

Acknowledgments

This study was performed with the support of the COST EU project NEUROMATH (BM 0601) and supported partially by the European ICT Programme Project FP7-224631. 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. Luciano da F. Costa thanks CNPq (301303/06-1) and FAPESP (05/00587-5) for sponsorship. Francisco Aparecido Rodrigues is grateful to FAPESP (07/50633-9).

References

  1. Achard S, Bullmore E (2007) Efficiency and cost of economical brain functional networks. PloS Comput Biol 3(2):e17CrossRefPubMedGoogle Scholar
  2. Astolfi L, Cincotti F, Mattia D, De Vico Fallani F, Salinari S, Ursino M, Zavaglia M, Marciani MG, Babiloni F (2006) Estimation of the cortical connectivity patterns during the intention of limb movements. IEEE Eng Med Biol Mag 25(4):32–38CrossRefPubMedGoogle Scholar
  3. Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccalà L, De Vico Fallani F, Salinari S, Ursino M, Zavaglia M, Ding L, Edgar JC, Miller GA, He B, Babiloni F (2007) A comparison of different cortical connectivity estimators for high resolution EEG recordings. Hum Brain Mapp 28(2):143–157CrossRefPubMedGoogle Scholar
  4. Babiloni F, Babiloni C, Locche L, Cincotti F, Rossini PM, Carducci F (2000) High resolution EEG: source estimates of Laplacian-transformed somatosensory-evoked potentials using a realistic subject head model constructed from magnetic resonance images. Med Biol Eng Comput 38:512–519CrossRefPubMedGoogle Scholar
  5. Bartolomei F, Bosma I, Klein M, Baayen JC, Reijneveld JC, Postma TJ, Heimans JJ, van Dijk BW, de Munck JC, de Jongh A, Cover KS, Stam CJ (2006) Disturbed functional connectivity in brain tumour patients: evaluation by graph analysis of synchronization matrices. Clin Neurophysiol 117:2039–2049CrossRefPubMedGoogle Scholar
  6. Bassett DS, Meyer-Linderberg A, Achard S, Th Duke, Bullmore E (2006) Adaptive reconfiguration of fractal smallworld human brain functional networks. Proc Natl Acad Sci USA 103:19518–19523CrossRefPubMedGoogle Scholar
  7. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: Structure and dynamics. Phys Rep 424:175–308CrossRefGoogle Scholar
  8. Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198CrossRefPubMedGoogle Scholar
  9. Chavez M, Valencia M, Navarro V, Latora V, Martinerie J (2010) Functional modularity of background activities in normal and epileptic brain networks. Phys Rev Lett 104(11):118701CrossRefPubMedGoogle Scholar
  10. Costa LF, Rodrigues FA. (2008). Superedges: connecting structure and dynamics in complex networks, arXiv:0801.4068v2Google Scholar
  11. De Vico Fallani F, Astolfi L, Cincotti F, Mattia D, Marciani MG, Salinari S, Kurths J, Gao S, Cichocki A, Colosimo A, Babiloni F (2007) Cortical functional connectivity networks in normal and spinal cord injured patients: evaluation by graph analysis. Hum Brain Mapp 28:1334–1336CrossRefPubMedGoogle Scholar
  12. De Vico Fallani F, Astolfi L, Cincotti F, Mattia D, Marciani MG, Tocci A, Salinari S, Witte H, Hesse W, Gao S, Colosimo A, Babiloni F (2008) Cortical network dynamics during foot movements. Neuroinformatics 6(1):23–34CrossRefPubMedGoogle Scholar
  13. Duffau H (2006) Brain plasticity: From pathophysiological mechanisms to therapeutic applications. J Clin Neurosci 13:885–897CrossRefPubMedGoogle Scholar
  14. Eguiluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102CrossRefPubMedGoogle Scholar
  15. Gevins A, Le J, Martin N, Brickett P, Desmond J, Reutter B (1994) High resolution EEG: 124-channel recording, spatial deblurring and MRI integration methods. Electroencephalogr Clin Neurophysiol 39:337–358Google Scholar
  16. Goh KI, Kahng B, Kim D (2001) Universal behavior of load distribution in scale-free networks. Phys Rev Lett 87:278701CrossRefPubMedGoogle Scholar
  17. Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438CrossRefGoogle Scholar
  18. Kaminski M, Ding M, Truccolo WA, Bressler S (2001) Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol Cybern 85:145–157CrossRefPubMedGoogle Scholar
  19. Lago-Fernandez LF, Huerta R, Corbacho F, Siguenza JA (2000) Fast response and temporal coherent oscillations in small-world networks, Phys Rev Lett 84:2758–2761CrossRefPubMedGoogle Scholar
  20. Le J, Gevins A (1993) A method to reduce blur distortion from EEG’s using a realistic head model. IEEE Trans Biomed Eng 40:517–528CrossRefPubMedGoogle Scholar
  21. Maslov S, Sneppen K (2002) Specificity and stability in topology of protein networks. Science 296:910–913CrossRefPubMedGoogle Scholar
  22. Mattia D, Cincotti F, Astolfi L, De Vico Fallani F, Scivoletto G, Marciani M, Babiloni F (2009) Motor cortical responsiveness to attempted movements in tetraplegia: Evidence from neuroelectrical imaging. Clin Neurophysiol 120(1):181–189CrossRefPubMedGoogle Scholar
  23. Micheloyannis S, Pachou E, Stam CJ, Vourkas M, Erimaki S, Tsirka V (2006) Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis. Neurosci Lett 402:273–277CrossRefPubMedGoogle Scholar
  24. Milgram S (1967) The small world problem. Psychol Today 1:60–67Google Scholar
  25. Pfurtsheller G, Lopes da Silva FH (1999) Event-related EEG/EMG synchronizations and desynchronization: basic principles. Clin Neurophysiol 110:1842–1857CrossRefGoogle Scholar
  26. Ponten SC, Bartolomei F, Stam CJ (2007) Small-world networks and epilepsy: graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures. Clin Neurophysiol 118(4):918–927CrossRefPubMedGoogle Scholar
  27. Popivanov D, Mineva A, Krekule I (1999) EEG patterns in theta and gamma frequency range and their probable relation to human voluntary movement organization. Neurosci Lett 267:5–8CrossRefPubMedGoogle Scholar
  28. Rodrigues FA, Costa LD (2009) A structure-dynamic approach to cortical organization: Number of paths and accessibility. J Neurosci Methods 183(1):57–62CrossRefPubMedGoogle Scholar
  29. Rossini PM (2000) Brain redundancy: responsivity or plasticity? Ann Neurol 48(1):128–130CrossRefPubMedGoogle Scholar
  30. Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E (2005) Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 15(9):1332–1342CrossRefPubMedGoogle Scholar
  31. Sporns O (2002) Graph theory methods for the analysis of neural connectivity patterns. In: Kötter R (ed) Neuroscience databases A practical guide. Kluwer, Boston, pp 171–186Google Scholar
  32. Sporns O, Tononi G, Edelman GE (2000) Connectivity and complexity: the relationship between neuroanatomy and brain dynamics. Neural Netw 13:909–922CrossRefPubMedGoogle Scholar
  33. Stam CJ (2004) Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? Neurosci Lett 355:25–28CrossRefPubMedGoogle Scholar
  34. Stam CJ, Jones BF, Manshanden I, van Walsum AM, Montez T, Verbunt JP, de Munck JC, van Dijk BW, Berendse HW, Scheltens P (2006) Magnetoencephalographic evaluation of resting-state functional connectivity in Alzheimer’s disease. Neuroimage 32:1335–1344CrossRefPubMedGoogle Scholar
  35. Stam CJ, Jones BF, Nolte G, Breakspear M, Scheltens Ph (2007) Small-world networks and functional connectivity in Alzheimer’s disease. Cereb Cortex 17:92–99CrossRefPubMedGoogle Scholar
  36. Stephan KE, Hilgetag C-C, Burns GAPC, O’Neill MA, Young MP, Kotter R (2000) Computational analysis of functional connectivity between areas of primate cerebral cortex. Phil Trans R Soc Lond B 355:111–126CrossRefGoogle Scholar
  37. Strogatz SH (2001) Exploring complex networks. Nature 410:268–276CrossRefPubMedGoogle Scholar
  38. Tononi G, Sporns O, Edelman GM (1994) A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc Natl Acad Sci USA 91:5033–5037CrossRefPubMedGoogle Scholar
  39. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442CrossRefPubMedGoogle Scholar
  40. Zar JH (1984) Biostatistical analysis. Prentice Hall, Englrwood CliffsGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Fabrizio De Vico Fallani
    • 1
    • 2
  • Francisco Aparecido Rodrigues
    • 3
  • Luciano da Fontoura Costa
    • 5
  • Laura Astolfi
    • 1
    • 4
  • Febo Cincotti
    • 1
  • Donatella Mattia
    • 1
  • Serenella Salinari
    • 4
  • Fabio Babiloni
    • 1
    • 2
  1. 1.Laboratory of Clinical NeurophysiopathologyIRCCS “Fondazione Santa Lucia”RomeItaly
  2. 2.Department of Human Physiology and PharmacologyUniversity “Sapienza”RomeItaly
  3. 3.Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão PauloBrazil
  4. 4.Department of Informatica e SistemisticaUniversity “Sapienza”RomeItaly
  5. 5.Instituto de Física de São CarlosUniversidade de São PauloSão PauloBrazil

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