Abstact
In this chapter, we address the challenge of detecting interactions among neuronal processes by means of bivariate and multivariate linear analysis techniques. For linear systems, both undirected and directed measures exist. Coherence is a commonly used undirected bivariate measure to detect the interaction between two nodes of a network, while multivariate measures like the partial coherence distinguish direct and indirect connections. The partial directed coherence additionally features the direction influences between nodes. We introduce the theoretical framework of these analysis techniques, discuss their estimation, and present their application to simulated and real-world data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Akaike. A new look at the statistical model identification. IEEE Trans. Automat. Contr., AC-19:716–723, 1974.
L. A. Baccalá and K. Sameshima. Partial directed coherence: a new concept in neural structure determination. Biol. Cybern., 84:463–474, 2001.
P. Bloomfield. Fourier Analysis of Time Series: An Introduction. John Wiley & Sons, New York, 1976.
D. R. Brillinger. Time Series: Data Analysis and Theory. Holden-Day, San Francisco, 1981.
P. J. Brockwell and R. A. Davis. Time Series: Theory and Methods. Springer, New York, 1998.
R. Dahlhaus. Graphical interaction models for multivariate time series. Metrika, 51:157–172, 2000.
R. Dahlhaus and M. Eichler. Causality and graphical models for time series. In P. Green, N. Hjort, and S. Richardson, editors, Highly Structured Stochastic Systems, pp. 115–137. Oxford University Press, Oxford, 2003.
M. Eichler. A graphical approach for evaluating effective connectivity in neural systems. Phil. Trans. R. Soc. B, 360:953–967, 2005.
M. Eichler. Graphical modeling of dynamic relationships in multivariate time series. In B. Schelter, M. Winterhalder, and J. Timmer, editors, Handbook of Time Series Analysis, Chapter 14, pp. 335–372. Wiley-Vch, Weinheim, 2006.
J. Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37:424–438, 1969.
E. J. Hannan. Multiple Time Series. Handbook of Statistics. Wiley, New York, 1970.
E. L. Lehmann. Testing Statistical Hypotheses. Springer, New York, 1997.
H. Lütkepohl. Introduction to Multiple Time Series Analysis. Springer, Berlin 1993.
A. Neumaier and T. Schneider. Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans. Math. Softw., 27:27–57, 2001.
M. B. Priestley. Spectral Analysis and Time Series. Academic Press, London, 1989.
B. Schelter, M. Winterhalder, R. Dahlhaus, J. Kurths, and J. Timmer. Partial phase synchronization for multivariate synchronizing systems. Phys. Rev. Lett., 96:208103, 2006a.
B. Schelter, M. Winterhalder, M. Eichler, M. Peifer, B. Hellwig, B. Guschlbauer, C. H. Lücking, R. Dahlhaus, and J. Timmer. Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Methods, 152:210–219, April 2006b.
B. Schelter, M. Winterhalder, B. Hellwig, B. Guschlbauer, C. H. Lücking, and J. Timmer. Direct or indirect? Graphical models for neural oscillators. J. Physiol. Paris, 99:37–46, January 2006c.
B. Schelter, M. Winterhalder, J. Kurths, and J. Timmer. Phase synchronization and coherence analysis: Sensitivity and specificity. Int. J. Bif. Chaos, 17:3551–3556, 2007.
T. Schneider and A. Neumaier. Algorithm 808: ARfit – A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans. Math. Softw., 27:58–65, 2001.
J. Timmer, M. Lauk, S. Häuβler, V. Radt, B. Köster, B. Hellwig, B. Guschlbauer, C. H. Lücking, M. Eichler, and G. Deuschl. Cross-spectral analysis of tremor time series. Int. J. Bif. Chaos, 10:2595–2610, 2000.
M. Winterhalder, B. Schelter, W. Hesse, K. Schwab, L. Leistritz, D. Klan, R. Bauer, J. Timmer, and H. Witte. Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems. Sig. Proc., 85:2137–2160, 2005.
M. Winterhalder, B. Schelter, J. Kurths, A. Schulze-Bonhage, and J. Timmer. Sensitivity and specificity of coherence and phase synchronization analysis. Phys. Lett. A, 356:26–34, 2006.
M. Winterhalder, B. Schelter, and J. Timmer. Detecting coupling directions in multivariate oscillatory systems. Int. J. Bif. Chaos, 17:3735–3739, 2007.
Acknowledgments
Special thanks goes to Bernhard Hellwig, Florian Amtage, and Professor Carl Hermann Lücking who provided us not only with the tremor data but also with knowledge about the neurophysiology of Parkinsonian tremor. This work was supported by the German Science Foundation (Ti315/2-1) and by the German Federal Ministry of Education and Research (BMBF grant 01GQ0420).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Schad, A. et al. (2009). Approaches to the Detection of Direct Directed Interactions in Neuronal Networks. In: Velazquez, J., Wennberg, R. (eds) Coordinated Activity in the Brain. Springer Series in Computational Neuroscience, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-0-387-93797-7_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-93797-7_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-93796-0
Online ISBN: 978-0-387-93797-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)