Detecting effective connectivity in networks of coupled neuronal oscillators
The application of data-driven time series analysis techniques such as Granger causality, partial directed coherence and phase dynamics modeling to estimate effective connectivity in brain networks has recently gained significant prominence in the neuroscience community. While these techniques have been useful in determining causal interactions among different regions of brain networks, a thorough analysis of the comparative accuracy and robustness of these methods in identifying patterns of effective connectivity among brain networks is still lacking. In this paper, we systematically address this issue within the context of simple networks of coupled spiking neurons. Specifically, we develop a method to assess the ability of various effective connectivity measures to accurately determine the true effective connectivity of a given neuronal network. Our method is based on decision tree classifiers which are trained using several time series features that can be observed solely from experimentally recorded data. We show that the classifiers constructed in this work provide a general framework for determining whether a particular effective connectivity measure is likely to produce incorrect results when applied to a dataset.
KeywordsGranger causality Partial directed coherence Phase dynamics modeling Effective connectivity Neuronal oscillators Decision tree classifiers
This work was partially funded from the start-up funding to SST through the Dept of Pediatrics at UF and the startup funding to WOO and alumina fellowship to ERB through the Dept of Biomedical Eng at UF. SST and PRC were partially funded through the Children’s Miracle Network Funds and Eve and B. Wilder Center of Excellence for Epilepsy Research. PPK was partially funded through the Eckis Professor Endowment at the University of Florida. We appreciate constructive feedback from Dr. Alex Cadotte. We also acknowledge the generosity of Dr CJ Frazier for allowing access to his electrophysiology rig set up and Ms. Aishwarya Parthasarthy for assistance in setting up the dynamic clamp and collection of experimental datasets. We finally acknowledge assistance from Mr. Kyungpyo Hong in generating Fig. 2 of the manuscript.
- Baccala, L., Sameshima, K., & Takahashi, D. (2007). Generalized partial directed coherence. In Proceedings of the 15th international conference on digital signal processing, Cardiff, Wales, UK (pp. 163–166).Google Scholar
- Box, G., Jenkins, G., & Reinsel, G. (2008). Time series analysis: Forecasting and control (4th ed.). Hoboken: Wiley.Google Scholar
- Breiman, L., Friedman, J., Stone, C., & Olshen, R. (1984). Classification and regression trees. New York: Chapman and Hall.Google Scholar
- Brovelli, A., Ding, M., Ledberg, A., Chen, Y., Nakamura, R., & Bressler, S. (2004). Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by granger causality. Proceedings of the National Academy of Sciences of the United States of America, 101(26), 9849–9854.PubMedCrossRefGoogle Scholar
- Davidson, R., & MacKinnon, J. (2003). Econometric theory and methods. Oxford: Oxford University Press.Google Scholar
- Ding, M., Chen, Y., & Bressler, S. (2006). Granger causality: basic theory and application to neuroscience. In B. Schelter, M. Winterhalder, & J. Timmer (Eds.), Handbook of time series analysis (p. 451). Weinheim: Wiley-VCH.Google Scholar
- Fanselow, E. E., Sameshima, K., Baccala, L. A., & Nicolelis, M. A. (2001). Thalamic bursting in rats during different awake behavioral states. Proceedings of the National Academy of Sciences of the United States of America, 98(26), 15330–15335. doi: 10.1073/pnas.261273898.PubMedCrossRefGoogle Scholar
- Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77(378), 304.Google Scholar
- Geweke, J. (1984). Measures of conditional linear dependence and feedback between time series. Journal of the American Statistical Association, 79(388), 907–915.Google Scholar
- Izhikevich, E. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge: MIT Press.Google Scholar
- Lecar, H. (2007). Morris–lecar model. Scholarpedia, 2, 1333. www.scholarpedia.com.
- Lütkepohl, H. (2010). New introduction to multiple time series analysis. New York: Springer.Google Scholar
- Pikovsky, A., Rosenblum, M., & Kurths, J. (2002). Synchronization: A universal concept in nonlinear sciences. Cambridge: Cambridge University Press.Google Scholar
- Schaffer, C. (1993). Selecting a classification method by cross-validation. Machine Learning, 13, 135–143.Google Scholar
- Sporns, O. (2010). Networks of the brain. Cambridge: MIT Press.Google Scholar