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


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.


Connectivity Causality Neuronal networks Partial directed coherence 



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


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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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