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Biological Cybernetics

, Volume 113, Issue 3, pp 309–320 | Cite as

Evaluation of connectivity estimates using spiking neuronal network models

  • Ronaldo V. NunesEmail author
  • Marcelo B. Reyes
  • Raphael Y. de Camargo
Original Article

Abstract

The flow of information between different regions of the cortex is fundamental for brain function. Researchers use causality detection techniques, such as Granger causality, to infer connectivity among brain areas from time series. Generalized partial directed coherence (GPDC) is a frequency domain linear method based on vector autoregressive model, which has been applied in electroencephalography, local field potential, and blood oxygenation level-dependent signals. Despite its widespread usage, previous attempts to validate GPDC use oversimplified simulated data, which do not reflect the nonlinearities and network couplings present in biological signals. In this work, we evaluated the GPDC performance when applied to simulated LFP signals, i.e., generated from networks of spiking neuronal models. We created three models, each containing five interacting networks, and evaluated whether the GPDC method could accurately detect network couplings. When using a stronger coupling, we showed that GPDC correctly detects all existing connections from simulated LFP signals in the three models, without false positives. Varying the coupling strength between networks, by changing the number of connections or synaptic strengths, and adding noise in the times series, altered the receiver operating characteristic (ROC) curve, ranging from perfect to chance level retrieval. We also showed that GPDC values correlated with coupling strength, indicating that GPDC values can provide useful information regarding coupling strength. These results reinforce that GPDC can be used to detect causality relationships over neural signals.

Keywords

Connectivity Causality Neuronal networks Partial directed coherence 

Notes

Acknowledgements

This study was supported by Federal University of ABC (UFABC) and Coordination for the Improvement of Higher Education Personnel (CAPES).

References

  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723Google Scholar
  2. Akam T, Kullmann DM (2010) Oscillations and filtering networks support flexible routing of information. Neuron 67(2):308–320Google Scholar
  3. Akam T, Kullmann DM (2014) Oscillatory multiplexing of population codes for selective communication in the mammalian brain. Nat Rev Neurosci 15(2):111–122Google Scholar
  4. Baccalá LA, Sameshima K, Takahashi D (2007) Generalized partial directed coherence. In: 2007 15th International conference on digital signal processing. IEEE, pp 163–166Google Scholar
  5. Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84(6):463–474Google Scholar
  6. Barnett L, Seth AK (2014) The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. J Neurosci Methods 223:50–68Google Scholar
  7. Bastos AM, Schoffelen JM (2016) A tutorial review of functional connectivity analysis methods and their interpretational pitfalls. Front Syst Neurosci 9:175Google Scholar
  8. Bastos AM, Vezoli J, Fries P (2015) Communication through coherence with inter-areal delays. Curr Opin Neurobiol 31:173–180Google Scholar
  9. Bernasconi C, König P (1999) On the directionality of cortical interactions studied by structural analysis of electrophysiological recordings. Biol Cybern 81(3):199–210Google Scholar
  10. Brovelli A, Ding M, Ledberg A, Chen Y, Nakamura R, Bressler SL (2004) Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. Proc Natl Acad Sci USA 101(26):9849–9854Google Scholar
  11. Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186–198Google Scholar
  12. Buzsáki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407Google Scholar
  13. Cadotte AJ, DeMarse TB, He P, Ding M (2008) Causal measures of structure and plasticity in simulated and living neural networks. PloS ONE 3(10):e3355Google Scholar
  14. Cadotte AJ, DeMarse TB, Mareci TH, Parekh MB, Talathi SS, Hwang DU, Ditto WL, Ding M, Carney PR (2010) Granger causality relationships between local field potentials in an animal model of temporal lobe epilepsy. J Neurosci Methods 189(1):121–129Google Scholar
  15. Campo AT, Martinez-Garcia M, Nácher V, Luna R, Romo R, Deco G (2015) Task-driven intra-and interarea communications in primate cerebral cortex. Proc Natl Acad Sci 112(15):4761–4766Google Scholar
  16. Cavallari S, Panzeri S, Mazzoni A (2014) Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks. Front Neural Circuits 8:12Google Scholar
  17. David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20(3):1743–1755Google Scholar
  18. David O, Cosmelli D, Friston KJ (2004) Evaluation of different measures of functional connectivity using a neural mass model. Neuroimage 21(2):659–673Google Scholar
  19. Einevoll GT, Kayser C, Logothetis NK, Panzeri S (2013) Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat Rev Neurosci 14(11):770Google Scholar
  20. Faes L, Nollo G (2010) Extended causal modeling to assess partial directed coherence in multiple time series with significant instantaneous interactions. Biol Cybern 103(5):387–400Google Scholar
  21. Friston KJ (2011) Functional and effective connectivity: a review. Brain Connect 1(1):13–36Google Scholar
  22. Gao L, Sommerlade L, Coffman B, Zhang T, Stephen JM, Li D, Wang J, Grebogi C, Schelter B (2015) Granger causal time-dependent source connectivity in the somatosensory network. Sci Rep 5(10):399Google Scholar
  23. Garofalo M, Nieus T, Massobrio P, Martinoia S (2009) Evaluation of the performance of information theory-based methods and cross-correlation to estimate the functional connectivity in cortical networks. PloS ONE 4(8):e6482Google Scholar
  24. Geweke J (1982) Measurement of linear dependence and feedback between multiple time series. J Am Stat Assoc 77(378):304–313Google Scholar
  25. Goñi J, van den Heuvel MP, Avena-Koenigsberger A, de Mendizabal NV, Betzel RF, Griffa A, Hagmann P, Corominas-Murtra B, Thiran JP, Sporns O (2014) Resting-brain functional connectivity predicted by analytic measures of network communication. Proc Natl Acad Sci 111(2):833–838Google Scholar
  26. Granger CW (1969) Investigating causal relations by econometric models and cross-spectral methods. Econom J Econom Soc 37(3):424–438Google Scholar
  27. Hamilton JD (1994) Time series analysis, vol 2. Princeton University Press, PrincetonGoogle Scholar
  28. Hoerzer GM, Liebe S, Schloegl A, Logothetis NK, Rainer G (2010) Directed coupling in local field potentials of macaque v4 during visual short-term memory revealed by multivariate autoregressive models. Front Comput Neurosci 4:14Google Scholar
  29. Hu B, Dong Q, Hao Y, Zhao Q, Shen J, Zheng F (2017) Effective brain network analysis with resting-state EEG data: a comparison between heroin abstinent and non-addicted subjects. J Neural Eng 14(4):046,002Google Scholar
  30. Ito S, Hansen ME, Heiland R, Lumsdaine A, Litke AM, Beggs JM (2011a) Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model. PLoS ONE 6(11):1–13Google Scholar
  31. Ito S, Hansen ME, Heiland R, Lumsdaine A, Litke AM, Beggs JM (2011b) Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model. PloS ONE 6(11):e27,431Google Scholar
  32. Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14(6):1569–1572Google Scholar
  33. Izhikevich EM (2006) Polychronization: computation with spikes. Neural Comput 18(2):245–282Google Scholar
  34. Kaminski M, Blinowska KJ (1991) A new method of the description of the information flow in the brain structures. Biol Cybern 65(3):203–210Google Scholar
  35. Kamiński M, Liang H (2005) Causal influence: advances in neurosignal analysis. Crit Rev Biomed Eng 33(4):347–430Google Scholar
  36. Kim S, Putrino D, Ghosh S, Brown EN (2011) A Granger causality measure for point process models of ensemble neural spiking activity. PLoS Comput Biol 7(3):e1001,110Google Scholar
  37. Koch C, Segev I (1988) Methods in neuronal modeling: from synapses to networks. MIT Press, CambridgeGoogle Scholar
  38. Lindén H, Tetzlaff T, Potjans TC, Pettersen KH, Grün S, Diesmann M, Einevoll GT (2011) Modeling the spatial reach of the LFP. Neuron 72(5):859–872Google Scholar
  39. Lopes dSF, Hoeks A, Smits H, Zetterberg L (1974) Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik 15(1):27Google Scholar
  40. Lowet E, Roberts MJ, Bonizzi P, Karel J, De Weerd P (2016) Quantifying neural oscillatory synchronization: a comparison between spectral coherence and phase-locking value approaches. PloS ONE 11(1):e0146,443Google Scholar
  41. Maris E, Oostenveld R (2007) Nonparametric statistical testing of EEG and MEG data. J Neurosci Methods 164(1):177–190Google Scholar
  42. Massaroppe L, Baccalá LA (2015) Kernel-nonlinear-PDC extends partial directed coherence to detecting nonlinear causal coupling. In: Engineering in medicine and biology society (EMBC), 2015 37th annual international conference of the IEEE. IEEE, pp 2864–2867Google Scholar
  43. Matias FS, Gollo LL, Carelli PV, Bressler SL, Copelli M, Mirasso CR (2014) Modeling positive Granger causality and negative phase lag between cortical areas. NeuroImage 99:411–418Google Scholar
  44. Mazzoni A, Panzeri S, Logothetis NK, Brunel N (2008) Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons. PLoS Comput Biol 4(12):e1000,239Google Scholar
  45. Mazzoni A, Brunel N, Cavallari S, Logothetis NK, Panzeri S (2011) Cortical dynamics during naturalistic sensory stimulations: experiments and models. J Physiol Paris 105(1–3):2–15Google Scholar
  46. Mazzoni A, Lindén H, Cuntz H, Lansner A, Panzeri S, Einevoll GT (2015) Computing the local field potential (LFP) from integrate-and-fire network models. PLOS Comput Biol 11(12):e1004,584Google Scholar
  47. Ning Y, Zheng R, Li K, Zhang Y, Lyu D, Jia H, Ren Y, Zou Y (2018) The altered Granger causality connection among pain-related brain networks in migraine. Medicine 97(10):e0102Google Scholar
  48. Omidvarnia A, Azemi G, Boashash B, OToole JM, Colditz PB, Vanhatalo S (2014) Measuring time-varying information flow in scalp EEG signals: orthogonalized partial directed coherence. IEEE Trans Biomed Eng 61(3):680–693Google Scholar
  49. Papana A, Kyrtsou C, Kugiumtzis D, Diks C (2013) Simulation study of direct causality measures in multivariate time series. Entropy 15(7):2635–2661Google Scholar
  50. Pascual-Marqui R, Biscay R, Bosch-Bayard J, Lehmann D, Kochi K, Yamada N, Kinoshita T, Sadato N (2014) Isolated effective coherence (iCoh): causal information flow excluding indirect paths. arXiv preprint arXiv:1402.4887
  51. Rodrigues PL, Baccalá LA (2016) Statistically significant time-varying neural connectivity estimation using generalized partial directed coherence. In: 2016 IEEE 38th annual international conference of the engineering in medicine and biology society (EMBC). IEEE, pp 5493–5496Google Scholar
  52. Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3):1059–1069Google Scholar
  53. Saito Y, Harashima H (1981) Tracking of information within multichannel EEG record causal analysis in EEG. In: Yamaguchi N, Fujisawa K (eds) Recent advances in EEG and EMG data processing. Elsevier, Amsterdam, pp 133–146Google Scholar
  54. Sameshima K, Baccalá LA (1999) Using partial directed coherence to describe neuronal ensemble interactions. J Neurosci Methods 94(1):93–103Google Scholar
  55. Sancristóbal B, Vicente R, Garcia-Ojalvo J (2014) Role of frequency mismatch in neuronal communication through coherence. J Computat Neurosci 37(2):193–208Google Scholar
  56. Santarnecchi E, Galli G, Polizzotto NR, Rossi A, Rossi S (2014) Efficiency of weak brain connections support general cognitive functioning. Hum Brain Mapp 35(9):4566–4582Google Scholar
  57. Sato JR, Takahashi DY, Arcuri SM, Sameshima K, Morettin PA, Baccalá LA (2009) Frequency domain connectivity identification: an application of partial directed coherence in fMRI. Hum Brain Mapp 30(2):452–461Google Scholar
  58. Schelter B, Timmer J, Eichler M (2009) Assessing the strength of directed influences among neural signals using renormalized partial directed coherence. J Neurosci Methods 179(1):121–130Google Scholar
  59. Seidler R, Erdeniz B, Koppelmans V, Hirsiger S, Mérillat S, Jäncke L (2015) Associations between age, motor function, and resting state sensorimotor network connectivity in healthy older adults. NeuroImage 108:47–59Google Scholar
  60. Seth AK (2010) A MATLAB toolbox for Granger causal connectivity analysis. J Neurosci Methods 186(2):262–273Google Scholar
  61. Shakil S, Lee CH, Keilholz SD (2016) Evaluation of sliding window correlation performance for characterizing dynamic functional connectivity and brain states. NeuroImage 133:111–128Google Scholar
  62. Shao PC, Huang JJ, Shann WC, Yen CT, Tsai ML, Yen CC (2015) Granger causality-based synaptic weights estimation for analyzing neuronal networks. J Comput Neurosci 38(3):483–497Google Scholar
  63. Shim WH, Baek K, Kim JK, Chae Y, Suh JY, Rosen BR, Jeong J, Kim YR (2013) Frequency distribution of causal connectivity in rat sensorimotor network: resting-state fMRI analyses. J Neurophysiol 109(1):238–248Google Scholar
  64. Sommariva S, Sorrentino A, Piana M, Pizzella V, Marzetti L (2017) A comparative study of the robustness of frequency-domain connectivity measures to finite data length. Brain topography pp 1–21Google Scholar
  65. Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of computational modelling in neuroscience. Cambridge University Press, CambridgeGoogle Scholar
  66. Takahashi DY, Baccalá LA, Sameshima K (2008) Partial directed coherence asymptotics for var processes of infinite order. Int J Bioelectromagn 10(1):31–36Google Scholar
  67. Thomson DJ (1982) Spectrum estimation and harmonic analysis. Proc IEEE 70(9):1055–1096Google Scholar
  68. Tomov P, Pena RF, Zaks MA, Roque AC (2014) Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types. Front Comput Neurosci 8:103Google Scholar
  69. Wang HE, Bénar CG, Quilichini PP, Friston KJ, Jirsa VK, Bernard C (2014) A systematic framework for functional connectivity measures. Front Neurosci 8:405Google Scholar
  70. Wu MH, Frye RE, Zouridakis G (2011a) A comparison of multivariate causality based measures of effective connectivity. Comput Biol Med 41(12):1132–1141Google Scholar
  71. Wu X, Zhou C, Wang J, Lu Ja (2011b) Detecting the topology of a neural network from partially obtained data using piecewise granger causality. In: International symposium on neural networks. Springer, pp 166–175Google Scholar
  72. Youssofzadeh V, Prasad G, Naeem M, Wong-Lin K (2016) Temporal information of directed causal connectivity in multi-trial ERP data using partial Granger causality. Neuroinformatics 14(1):99–120Google Scholar
  73. Zhang L, Chen G, Niu R, Wei W, Ma X, Xu J, Wang J, Wang Z, Lin L (2012) Hippocampal theta-driving cells revealed by Granger causality. Hippocampus 22(8):1781–1793Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Mathematics, Computing and CognitionUniversidade Federal do ABCSão Bernardo do CampoBrazil

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